The 21-year-old midfielder joins from Brazilian club Flamengo and signs a five-and-a-half year deal at Molineux, with the option of extending that by a further 12 months.
The move brings an end to a long transfer saga after French club Lyon tried to hijack the deal and Flamengo reneged on the deal they had already agreed with Wolves.
Gomes pushed to join Wolves and turned down Lyon, while Wolves stood firm on their original offer, which was eventually agreed.
Sporting director Matt Hobbs said: “It feels like it’s been forever, even though it’s only been a couple of weeks. In truth, it started back in August 2021 when our scouting coordinator Elliot Sutcliffe, who was covering South America at the time. When he first saw him, from the first viewing, he said he was one to keep an eye on, with an interesting profile.
“We’ve watched all his games since and got in touch with his agent in the last window to see what the situation was, so he’s always been a player on our list, who we’d like to sign at some stage.
“It’s well publicised that we thought we had a deal sorted a couple of weeks ago, but what’s been great, and probably what’s got the deal done, has been the player.
"He’s turned down a more lucrative offer at another club because he always said he gave his word, he always wanted to come to Wolves since talking to Julen and I, so he’s kept his word and stayed strong. Without the player taking the stance he did, we wouldn’t be in this situation.”