The 19-year-old has penned a five-year deal, Villa announced in a statement, and the transfer fee could rise to from an initial 10 million euros (£7.1million) to 12 million euros (£8.6million) if certain clauses are met.
Barcelona have a first refusal option on the winger and can buy him back during his first three years at Villa Park, the Spanish club have announced.
Villa manager Tim Sherwood said: "I've known him for a couple of years
I tried to see if it was possible to bring him to Tottenham when I was there.
"He is someone I have been tracking for a long time
He has played a lot of games for someone so young because he is physically a man.
"He is a big powerful boy, very quick, dynamic, a maverick type player, you never know what's going to come out next
Those players are very few and far between.
"He is not the finished article by any means
He is certainly a player who can help us out now, but for the long term future he is magnificent
"He is very dynamic
He stays wide, picks the ball up, runs at defenders and doesn't give them a minute's peace.
"I wouldn't like to compare him to any other player, hopefully he'll make his own name for himself and they will want to be the new Adama Traore."
Adama made 63 appearances for Barcelona B and, after coming up through the youth ranks at the Nou Camp, made four appearances for the first team, scoring once.
Sherwood travelled to Barcelona to convince the Spain Under-19 international to join Villa.
"I went to Barcelona and spoke to the representatives
We made a huge effort to bring him to the club
We showed him this is a great stage for him," Sherwood said, ahead of Villa's opening Barclays Premier League home game of the season against Manchester United on Friday.
"We recognise he needs developing and that I will give him as much development time as possible
We will give him a lot of work on the training field to improve what he already has."
Source : PA
Source: PA