The 19-year-old winger has been in England for 10 days looking at potential suitors and has chosen Villa over Stoke after he was rejected by Liverpool last week.
Barca will receive €9 million from Tim Sherwood's side and will retain a buy-back option on the talented midfielder, who has represented Spain at Under-19 level but chose to switch his international allegiance to Mali ahead of the U-20 World Cup earlier this year.
Adama made his first-team debut at the age of 17, replacing Neymar in a 4-0 win over Granada in November 2013. He scored his first goal for the Catalan club in an 8-1 win over Huesca in the Copa del Rey last December.
Meanwhile, the future of another Barca youngster, Croat Alen Halilovic, is up in the air after the 19-year-old rejected a loan move to Hamburg after the Bundesliga club refused to a clause in his contract guaranteeing him a certain amount of minutes.
Borussia Dortmund are also interested in taking the player on loan, as are Spanish sides Sporting Gijon and Celta Vigo, but the player prefers a move to the Bundesliga.
