Valencia president Manuel Llorente said they had accepted Barca's bid for the prized striker, who scored 21 league goals last season to finish his fifth consecutive campaign as the club's top scorer.
"There was a big offer from England that was not from Chelsea but Barcelona's was the best for us and the footballer," Llorente told a news conference.
"Villa has delivered a lot (to Valencia) and he deserves this chance."
FEATURE:Messi & Villa already on good terms
The 28-year-old is Spain's second-highest scorer with 36 goals from 55 matches, eight short of the record held by Real Madrid striker Raul, and he will be spearheading Spain's World Cup campaign in South Africa next month.
"This is without doubt the most difficult and emotive moment of my entire career," Villa said in a statement on Valencia's website.
"After five marvellous seasons I take away many feelings and leave behind many friends but also knowing that it is a good thing for the club.
"I have given my all for Valencia football club, which I will always have in my heart, of which I am a shareholder and which I wish all the luck in the world."
GUARANTEED GOALS
Barcelona confirmed the deal in a statement on their website, saying Villa would sign a four-year contract with an option for one more year.
The player, who Barca said "guaranteed goals", will travel to the Catalan capital on Thursday and will take a medical before being presented on Friday.
Nicknamed "el guaje" (the kid), Villa will join a formidable Barca forward line including La Liga's leading marksman Lionel Messi, Swede Zlatan Ibrahimovic, and Spaniards Pedro and Bojan Krkic.
France striker Thierry Henry spent most of last season on the bench and is expected to move on.
Barca sporting director Txiki Begiristain told the club's TV channel on Wednesday Villa was a similar player to Messi in that he could play as a centre forward or drift in from the right wing into goal-scoring positions.
"He has the profile of a player who makes very good diagonal runs and moves very well into space," Begiristain said.
Valencia have been forced into the sale by the precarious nature of their finances. They are burdened with debts of more than 500 million euros, they have a half-built new stadium and have yet to sell their current one, the Mestalla.
"The board's principle objective is to make sure we have economic viability for the future," Llorente said, adding that he did not rule out further sales.
"We are obliged to take responsible decisions. Considering our situation it is responsible to sell this player.
"As everyone knows we could have done this deal last year but we thought at that moment it was best to ke
