The 25-year-old right-back will officially join the Championship outfit on July 1 following the expiration of his contract at Eintracht Braunschweig.
"It's crazy for me and it's the first time for me that I've signed for a club that's not in Germany," Ofosu-Ayeh told the club's official website. "I'm very excited about everything - the club, the fans and my teammates so I'm ready for my journey here. When I was made aware that there was interest from Wolves, I was very happy because I was injured and I couldn't perform well for my team.
"I was thinking about where I could play next season and then I heard from Wolves - for me it was always a dream to play in England and now I've seen everything here, I know that it's a very big club and a traditional club. I'm very happy that I have the chance to play here.
"It's all happened pretty quickly but sometimes that's better than it taking three or four months - I like it like that. The season finished but I have been injured for five weeks but I'm ready to play now. I know some guys who played in the Championship but it's difficult to compare how they adapted unless you've actually played in this league - we will just have to wait and see, I don't want to talk too much, I'd prefer to show my performances on the pitch.
"I've always been a fan of English football - I like the physical game, I think it's more physical than in Germany and I like that because I'm a physical player. I'm curious to find out how the league is now. I think the league will suit my style of play and I hope I can show everyone that."