The former Barcelona youngster has signed a five-year deal with the newly-promoted outfit after two seasons at the Riverside Stadium.
In 71 appearances he scored five goals and laid on 10 assists for Boro, though his breathtaking speed ensured he was always a threat for opposition defences.
He is just the latest high-profile signing at Molineux this summer, with Joao Moutinho and Rui Patricio among those to have joined up with Nuno's squad during the summer of 2018.
In total he becomes the club's fifth signing of the transfer window, with full-back Jonny Castro and forward Raul Jimenez having also been brought in by the Championship winners.
Traore began his career at Camp Nou but struggled to break through - making just four appearances for the senior team.
He suffered relegation again during his first campaign with Middlesbrough in 2016-17 but was one of the Championship's most dangerous attackers as Tony Pulis' team finished fifth, only to be knocked out in the play-offs by Villa.
Traore could now make his Wolves debut on Saturday as they host Everton in their first match back in the top flight.