The La Liga champions announced on their website that the deal will cost up to 5.1million euros (4.4million) with Barca receiving 50 per cent of any future transfer fee.
The 31-year-old Spain international joined Barca from Valencia in 2010 but has been wildly linked with a move away from the Nou Camp over recent months after struggling to tie down a first-team berth at the Catalan club last season.
Barca announced in a statement on their website: "Barca and the Madrid club have reached an agreement in principle for the transfer of the Asturian player.
"The deal will cost a maximum of 5.1million euros, with 2.1million this season, 2million more if the player is still at Atletico Madrid in the 2014/15 season and another million if he stays until the 2015/16 season.
"As well as that, Barca have reserved 50 per cent of the rights of any future transfer of the player."
Monday's announcement comes after Barca last month completed the signing of Brazil superstar forward Neymar in a 57million euros transfer from Santos, bolstering an attack that also includes Lionel Messi, Pedro Rodriguez and Alexis Sanchez.
Villa, who had been linked with a number of Barclays Premier League sides, joined Barca in a 40 million euros deal from Valencia in the summer of 2010, penning a four-year contract at the Nou Camp.
During his three years with the Catalan club, Spain's record goalscorer played 119 official games and scored 48 goals.
However, he spent eight months on the sidelines after suffering a broken leg during the Club World Cup in December 2011, forcing him to miss the second half of the 2011/12 season for Barca and also Spain's successful Euro 2012 campaign.
He made his Barca comeback in a pre-season friendly against Dinamo Bucharest last August and would go on to start 24 matches in all competitions for Tito Vilanova's men in the 2012/13 season with a further 16 appearances off the bench, scoring 16 goals.
Villa will leave Barca having helped the club win eight trophies in three years, including two Primera Division crowns and the 2011 Champions League.
It could be that one of Villa's first competitive games for Atletico will be against Barca, with the Copa del Rey winners meeting the La Liga champions in the Spanish Supercopa in August.
Atletico also confirmed the deal for Villa, who has scored 56 goals in 92 internationals for Spain, in a statement on their official website.
It read: "Atletico Madrid and Barcelona have reached an agreement in principle for the transfer of striker David Villa.
"This agreement will be consolidated once the Asturian player undertakes his medical and signs his contract with our club."