The 23-year-old Alba, who can also play as a winger, has been one of revelations of Euro 2012 after standing out because of his speed.
His run down the left flank and well-placed cross for Xabi Alonso’s header gave Spain its opening goal in the 2-0 win over France in the quarterfinals.
‘We are happy with (Alba),’ Spain coach Vicente del Bosque said. ‘We have found a specialist that has many years in front of him.
‘Yesterday (against Portugal), he knew how to handle the circumstances and did everything a fullback must do.’
Alba is a product of Barcelona’s La Masia football academy, like many of his new teammates, including Lionel Messi, Andres Iniesta and Xavi Hernandez. He is the latest former youth player the club has brought back following Cesc Fabregas, who returned from Arsenal last year.
The Barcelona native trained at La Masia from 1998-2005 before joining Valencia and helping the club finish in third place for the past three seasons.
He played 74 games and scored five goals in his three seasons with Valencia.
Alba is Barcelona’s first signing of the offseason. He will fill a hole in its defence left by Eric Abidal, who is recovering from a liver transplant.
Barcelona failed to make any major signing to bolster its defence during the past two offseasons, forcing midfielder Javier Mascherano to be converted into a central defender.