The Algerian international has moved to the Premier League rivals in a move worth up to more than £36million, ending five years at Molineux.
And in a post on Instagram after the move was announced, Ait-Nouri praised the club and supporters for welcoming him to England back in 2020.
Ait-Nouri said: "Five years - it's not easy to say goodbye.
"From the first day, you made me feel at home. You gave me the support and love that every footballer hopes to find, and I never took that for granted.
"I gave my all every time I wore the shirt - and for the team, the club, and for you.
"There were tough moments, but they only made me realise how much this place meant to me.
"Thank you for everything. For the memories, the support, and for making these years so special.
"I'll always carry Wolves with me."