The 23-year-old Alba, who is currently on international duty at Euro 2012, will pen a five-year contract once he has passed his medical, Barca have confirmed.
A Barcelona statement on the club's website read: "Barcelona announce that today they reached an agreement with Valencia for the transfer of Jordi Alba, who will undergo his medical next week.
"The cost of the operation will be 14million euros and the player will sign a contract for the next five seasons.
Attacking left-back Alba, whose contract with Valencia was due to expire in June 2013, is no stranger to Barcelona.
Born in the Catalan city of L'Hospitalet, Alba spent seven years at Barca's famous La Masia youth academy from 1998 to 2005.
Afterwards he played for local lower-league side Cornella for two years before joining Valencia in 2007.
At the Mestalla, Alba was part of the Valencia reserve side that was promoted to Segunda B before spending the 2008/09 season on loan at Gimnastic Tarragona.
On returning to Valencia he soon became a regular in coach Unai Emery's first team, making 74 league appearances in three seasons, scoring five goals.
That earned him international recognition, with his debut coming against Scotland last October. He has won 10 caps to date and has been an ever-present in Spain's five Euro 2012 matches so far, helping them through to Sunday's final.
Alba is Barcelona's first signing of the summer as they build towards next season under new coach Tito Vilanova, who has replaced Pep Guardiola.