The 22-year-old joins for an undisclosed fee, although reports suggest it is in the region of £18million, and has signed a five-year deal.
He missed Boro's opening day draw with Millwall with a dislocated shoulder, however the injury isn't expected to sideline him for long.
Traore came through the Barcelona academy before signing for Aston Villa in 2015 where he spent a season, but fell out of favour and decamped to Middlesbrough.
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After failing to score in 27 Premier League appearances when Boro were relegated in 2017, he scored five goals in 36 matches as Tony Pulis' side were beaten by Villa in the play-off semi-final.
It will mean a huge profit for City, who bought Zinchenko for around £1.7million two years ago and are now set to receive £16million.
With the likes of Rui Patricio, Joao Moutinho and Raul Jimenez already on board, we'll certainly be keeping an interested eye on developments at Molineux this season.
Add to that Benik Afobe and Diogo Jota, and Wolves aren't going to relinquish their hard-earned Premier League status without a fight.