Cesc Fabregas and Fernando Torres were jubilant after Spain won their first trophy since 1964.
Both players started the Euro 2008 final against Germany, with Liverpool's Torres scoring the only goal in a 1-0 win.
Fabregas, who was substituted after an hour, said: "This is the greatest day of my football life. 44 years on and we have done it again. This is one of the best trophies you can have and it is one of your dreams.
"It was a long time since a team of that quality, trying to get the ball on the ground and play beautiful football, went on to glory.
"Now we have made it - and you can [see] how young we are - we can now go on to fight for the World Cup in two years' time."
Fabregas and Torres were both named in the official squad of the tournament.
"It's a dream come true," Torres admitted. "At last justice has been done because the team that played the best football won the tournament.
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"I feel a tremendous joy. It still hasn't sunk in what we've achieved.
"This is my first title and I hope it's the first of many. We are used to watching finals on television, but today we were here and we won.
"The team that has played the best football in the tournament has won the title and now we have a place in European football history."
Chelsea midfielder Michael Ballack played the whole match for Germany but lost his third final of 2008, having been on the losing side for the Blues in the Carling Cup and Champions League showpieces.
Ballack said: "We had a great tournament, but made one mistake too many. We were lacking power against a great Spanish team, we couldn't keep up with them.
"It's always disappointing to lose a final, but we played a great championship. We wanted more, but we couldn't deliver. Still, we can be proud."