The Black Country side activated a release clause in the Spain U21 international's contract allowing them to speak to the player, who eventually agreed a five-year deal with the club.
The 22-year-old shone for Boro last season, scoring five goals and laying on 12 assists as the club reached the Championship play-off semi-finals.
Traore came through the academy at Barcelona, before joining Aston Villa in 2015.
Their relegation saw him move to Teesside a year later, where he quickly became a popular figure with the fans.
Boro had been hoping to keep the flying flanker with the club this summer and offered him a bumper new deal, but the lure of the Premier League proved too much for Traore.
Traore becomes Wolves' fifth signing of the summer following the arrivals of Rui Patricio, Jonny Castro Otto, Joao Moutinho and Raul Jimenez.
8 August 2018