The Spain international will move to the Vicente Calderon, subject to the agreement of personal terms and passing of a medical, in a deal worth an estimated 4.4 million pounds, with over half being paid if Villa remains an Atletico player during the 2014-15 and 2015-16 campaigns.
The Catalan club will also retain 50 percent from any future transfer involving the former Valencia striker.
Tottenham had emerged as the front runner to sign the 31-year-old attacker, but Atletico appears to have topped Spurs and won the race for his signature. The Spanish side is searching for a replacement for Radamel Falcao, who sealed a big-money move to Monaco back in May.
The Madrid club, which finished third in La Liga last season, had been in the hunt for Sevilla striker Alvaro Negredo, but Manchester City now appears to be the favorite to sign the 27-year-old Spaniard, with top target Edinson Cavani expected to join Paris Saint-Germain.
Villa joined Barca in 2010 from fellow La Liga side Valencia and has scored 48 goals in 119 appearances across all competitions.