Gomes made 130 appearances for Wolves after joining from Flamengo in 2023, scoring seven goals and featuring 41 times last season, form that saw him named the club's Player of the Year despite Wolves finishing bottom of the Premier League.
Wolves technical director Matt Jackson paid tribute to the departing midfielder.
"Joao deserves everything he gets from the game. He's a model professional, a lovely young man and a great family man.
"He's the type of professional coaches love and players love, so he will go on to be the outstanding player that we know he is.
"We're obviously sorry to see him go, but we have to take responsible decisions for the football club, and then we build to be stronger collectively.
"It's a very natural part of football - the best run football clubs who don't have unlimited resources have to work this way.
"The model is something that we have to adopt, and our fans have always been hugely understanding of that."
The Brazil international's arrival gives Unai Emery a ready-made option to cover for Amadou Onana, who is out until next year after suffering a serious knee injury with Belgium at the World Cup. Atletico Madrid had also been keen on Gomes, but the 25-year-old left Wolves' training camp in Portugal on Thursday to have a medical and finalise his switch to Villa Park.
Gomes joins for an initial £34m with a further £4m in add-ons, arriving as Villa continue to reshape their engine room following the £35m sale of Youri Tielemans to Manchester United, with fellow midfielder Morgan Rogers also set to leave after a £117m deal was agreed with Chelsea.
The Brazilian's ball-winning and pressing qualities are viewed as a close stylistic match for Onana, giving Emery a like-for-like option in the middle of the park while the Belgian recovers.
Aston Villa's recruitment drive shows little sign of slowing, with the club having moved quickly to identify Gomes as their next midfield target even before the Manzambi deal was finalised, reflecting the scale of the rebuild Emery is undertaking in that area of the pitch this summer.