Traore, a product of Barcelona's famed La Masia academy, is Boro's 11th signing of the close season.
Villa signed the 20-year-old Spaniard from Barcelona last August, and he made 11 league appearances for the club, all of them as a substitute, as the team were relegated from the top flight.
Traore's only goal for Villa came in his solitary start in the League Cup against Notts County last August.
"He is another important player and I am expecting a lot from him," Boro manager Aitor Karanka told the club's website (www.mfc.co.uk).
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"I've known him since he was a kid ... His level is higher than he showed last season, but in the right environment I'm hoping that he will show what he is capable of."
(Reporting by Simon Jennings in Bengaluru,; Editing by Neville Dalton)
