Torres struck in the first half as Spain beat Germany 1-0 in Vienna to win their first major trophy for 44 years and Torres's first trophy of any kind.
The Liverpool striker said: "I feel a tremendous joy. It still hasn't sunk in what we've achieved with this victory.
"The team that played the best football at Euro 2008 won the title and we have a place in European football history."
He added: "It's just a dream come true. This is my first title and I hope it's the first of many. "Victory in a Euro, it is almost as big as a World Cup. We are used to watching finals on television, but today we were here and we won.

Torres was soaked in champagne by his team-mates
"My job is to score goals. I want to win more titles and be the most important player in Europe and the world."
Coach Luis Aragones, who now steps down after four years in the job, paid tribute to Torres after the final whistle.
"Fernando is a great player for Liverpool and for our team and he can go anywhere because he has really extraordinary speed and he knows how to dribble," said the 69-year-old.
"We always tell him he's a player who is so young that he can learn to do everything and there is no doubt he can be one of the best players in the world."
Aragones, who could barely contain his delight with his side's resounding victory, believes the way they won the tournament may inspire other teams to try and play the same brand of football in the future.
"All those that love football want to see it played that way," he said. "People want players who can pass well and get into the penalty area and score goals.
"They'll look up to Spain as a model of how to play football.
"We've won this tournament brilliantly, it's a happy day for the players, the background staff, me, all Spaniards."
Arsenal midfielder Cesc Fabregas hailed his team's triumph as a "victory for beautiful football". The 21-year-old said: "It feels amazing, this is the best day of my life in football, I don't think we've realised yet what we have achieved.
"It's been a long time since a team playing this kind of beautiful football won a tournament like this.
"It is 44 years after Spain last won anything. This is one of the best trophies you can win as a footballer and I did it, we did it.

Fabregas hailed victory as the best day of his life
"We play football on the ground, we try to pass the ball and we won this tournament in style. We gave football the success it deserves.
"You know what a young squad this is, so hopefully we can think about winning the World Cup in two years' time."
Liverpool's Xabi Alonso, who came off the bench in the second half, added: "It feels great, of course - so many years without winning anything.
"It was very important for everyone - for the supporters, for the players, for the staff - and now we are absolutely happy and we want to enjoy the moment."

Thaksin Shinawatra arrived at Manchester City in July to a fund of goodwill from success-starved fans - now he risks every shred of his sporting reputation by sacking Sven-Goran Eriksson.The mere mention of Eriksson's name is the catalyst for a variety of a emotions after his time of under-achievement and excess personal baggage with England.And yet the Swede now, rightly, finds himself the subject an outpouring of sympathy as Thaksin prepares to make his sacking official.Before outlining the scale of mistake Thaksin is about to make, it is only right to go back to June last year when I wrote a piece insisting the former Thai Prime Minister was wrong to appoint Eriksson.He was right. And I was wrong. Now he is very wrong.I questioned whether Eriksson was a modern team-builder and whether he had the hunger and desire to do the job at Eastlands. It was a view coloured by watching his listless performances at three major tournaments in charge of England.Eriksson has answered those charges emphatically in a first season that has been one of undoubted progression, despite a fade-out in the second half of the campaign.He has also achieved the specific goal set for him by Thaksin - namely a top ten Premier League finish.Eriksson had to work the transfer market quickly and effectively when he took over because he was barely left with enough players after the departure of Stuart Pearce and the clock was ticking on the new season.Martin Petrov and Elano brought class and creativity, while Croatia's Vedran Corluka was another success.He made mistakes, namely the £8m paid for striker Rolando Bianchi, but when a workable squad has to be assembled swiftly from the wreckage of what had greeted him, the odd gamble will fail.If Eriksson made a fatal error, it may have been by blending his new players so quickly and starting the season so spectacularly.This appeared to raise the expectations of Thaksin, a man who appears to have a slender grasp on the realities of football if he feels Eriksson's performance this season warrants the sack.As I have stated, there is a helping of humble pie with these words because I believed Eriksson would be a failure at Eastlands after the England experiences.But he had started to rebuild his own and Manchester City's reputation this season - and this should have only been the start.City have worked hard in recent years to cast aside a name for snatching defeat from the jaws of victory.This has been done behind the scenes and Eriksson was in the process of putting matters right on the pitch. Thaksin is now about to throw so much good work away.Eriksson has also shown a willingness to give City's exciting crop of young players their chance and it was clear they had faith in him.Word from City is that Eriksson is a hugely popular figure, revered and respected by everyone at the club - except, it seems, by the man who matters.If Thaksin thinks his sacking of Eriksson is the decisive hands-on action the club's supporters revel in, he is guilty of a desperately bad misjudgement.City's fans, almost unanimously, are outraged by the news and the cynics might even suggest it is rather handy for Thaksin that the axe is falling after City's final home game.This spares him inevitable protests at Eastlands, although City fans will make their voices heard in support of Eriksson at Anfield and The Riverside in the final two games of his reign.Thaksin is apparently lining up Portugal coach Luiz Felipe Scolari - and while the Brazilian is a World Cup winner with his own country, what is his knowledge of the Premier League?Eriksson's departure has reportedly devastated City's squad. What now for them? What of all the players Eriksson brought in?Make no mistake, the law of football dictes that predators will now be circling the likes of Richard Dunne, Micah Richards, Martin Petrov and Elano, ready to make capital of the uncertainty and unrest.Will the new man want Eriksson's signings? Will Thaksin effectively have to start spending again?What will the new man have to spend? When will he be able to spend it? And will he be allowed to spend it on the men he wants?And - crucially - will Thaksin start the sacking game again next term if City fail to achieve what appear to be his farcially unrealistic expectations?Eriksson achieved Thaksin's goal of a top ten finish with something to spare and will still be sacked. Would any manager of consequence be in a rush to join City with that backdrop?Manchester City is a club crying out for stability on the pitch after the wilderness years and Eriksson could have provided it.Sadly, Thaksin has chosen to demonstrate his impatience and sporting naivety in one fell swoop in a move that has alienated fans only too willing to give him a chance.Manchester City's fans do not deserve that. Manchester City as a club does not deserve that. Eriksson does not deserve that either.It remains to be seen whether this is the defining moment of Thaksin's reign - but he is in the process of committing a major error.

Ryan Babel celebrates after scoring Liverpool's second goalLiverpool outclassed Derby to move to the top of the Premier League table for the first time under Rafa Benitez.
Xabi Alonso opened the scoring with a 45-yard free-kick that sailed straight into the net before Ryan Babel's turn gave him space for a superb second.
Fernando Torres' cool finish made it 3-0 and Alonso added a fourth with a rasping drive from the edge of the box.
Andrei Voronin tapped home to make it 5-0 and Andy Todd's mistake let in Torres to complete the rout.

It was an utterly dominant performance from the Reds, who have now won five out of their six games in all competitions this season - but none as easily as this.
They always looked like extending their impressive start to the season against a Derby side lacking ambition and devoid of ideas.
There was little to cheer Rams boss Billy Davies with his side merely hanging on from the start.

Bywater did well to keep out Agger's 25-yard shot after it clipped off Derby defender Robert Malcolm and had to dive to stop a Torres header soon after.
Liverpool then spent an unsuccessful spell trying their luck from distance but, when Alonso did break the deadlock on 27 minutes, it was also from long range.
The Spanish midfielder was not trying to find the net when he curled in a free-kick but Kuyt ran across Bywater's line of sight and the keeper could not react in time to keep the ball out.
Derby could probably count themselves slightly unlucky in the manner in which they conceded but they could not argue that Liverpool deserved their lead.
And there was nothing fortuitous about the way Babel made it 2-0 before the break with his first goal since his £11.5m summer move from Ajax.
The Dutchman collected the ball from Alvaro Arbeloa's pullback, bamboozled Andy Griffin and Claude Davis with his first touch and then buried the ball past Bywater for a goal of genuine class.
Things continued in the same vein after half-time and Alonso should have added to Liverpool's advantage when Arbeloa, Torres and Kuyt combined to tee him up with only Bywater to beat.

Torres celebrates after scoring Liverpool's third goal
A third goal duly arrived when Javier Mascherano fed Torres and the Spanish striker made for goal before slotting coolly home.
Derby simply had no answer to Liverpool's pace and movement going forward and, when another attack was not properly cleared, Alonso notched again with a precise shot into the bottom corner.
Torres was clearly enjoying himself too and he played a part in Liverpool's next goal, exchanging passes with Kuyt who saw his shot saved before substitute Voronin followed up to score.
And it was apt that Torres rounded off the scoring, nipping in when Todd failed to deal with Voronin's lobbed through ball and sliding the ball home.
A miserable day for Derby was summed up late on when Craig Fagan failed to make contact with the ball with only Jose Reina to beat and Davies will have few positives to take away from such a demoralising defeat.

The Galaxy turned on the style to welcome Beckham to LADavid Beckham has been officially unveiled as an LA Galaxy player to an audience of media and supporters at the club's Home Depot Stadium.
In a ceremony rich in American razzmatazz, several MLS and Galaxy figures praised Beckham.
The 32-year-old midfielder, wearing a grey suit, then rose from his seat as ticker tape flew into the sky.
He then held an LA Galaxy shirt and posed for photographs while the assembled fans chanted his name.

I think that potentially in the US soccer could be as big as everywhere else in the world
David Beckham
"I'm looking forward to starting training next week and my first game," said Beckham.
"I would like to say how honoured I am to be presented. It is nice to see so many fans.
"I have always looked for challenges and something exciting in my life.
"I think that potentially in the US soccer could be as big as everywhere else in the world."
But when Beckham made his first reference to the game he plays he said "foot.." before correcting himself and saying "soccer", adding "I'll get used to that at some point, I'm sorry".
Beckham's wife Victoria appeared before her husband and posed for photographers wearing a fuchsia pink dress and trademark black sunglasses.
Prior to Beckham's arrival a large video screen replayed highlights of Beckham's career.
As Galaxy general manager Alexi Lalas stood to address the gathered media and supporters, he was initially drowned out by the crowd chanting "Beckham, Beckham".

Supporters turned out in force to welcome Beckham
When the crowd calmed down, Lalas said the arrival of Beckham was an historic moment "not just for the Galaxy but for soccer and for the sport of soccer in the United States".
MLS commissioner Don Garber said: "Here in Los Angeles we have one of the world's most recognised athletes, most recognised players coming here to our league, our city, our team."
After Beckham spoke the mayor of Los Angeles, Antonio Villaraigosa, was introduced to the crowd, who welcomed him by booing loudly.
Villaraigosa then put on a Galaxy shirt and presented Beckham with a framed picture.
Beckham's first appearance for the Galaxy is scheduled to be a friendly against Premier League side Chelsea on 21 July.
The England midfielder has a five-year contract with Galaxy, who are currently struggling in second-bottom place in the MLS Western Division after 12 matches.

The club play at the 27,000-capacity Home Depot Center stadium in the south Los Angeles suburb of Carson.
Beckham will be paid $6.5m (£3.2m) by Galaxy this season, according to figures posted on the league's players' union website, and could make $250m (£123m) over the life of the contract in profit-sharing and sponsorship deals.
Beckham arrived in Los Angeles late on Thursday with his wife Victoria and three children - Brooklyn, Cruz and Romeo - but did not answer questions from the waiting media.
A series of media interviews and photo-shoots preceded their arrival, while a television programme documenting the family's move is set to air on US television on Monday.
The Beckhams will make their new home in a reported $22m (£10.8m), 13,000-square-foot villa in Beverly Hills, where neighbours include their friends Tom Cruise and Katie Holmes.