The move will become permanent for £34m at the end of the campaign.
Cunha is new Wolves manager Julen Lopetegui's first signing as he attempts to lift them off the foot of the Premier League table.
Cunha joined Atletico Madrid from Hertha Berlin in August 2021 and scored seven goals in 37 appearances across all competitions but has seen his minutes reduced this season, failing to score in 17 appearances.
A statement on the club's website read: 'Matheus Cunha will become Julen Lopetegui's first signing as Wolves head coach, joining on loan from January 1, subject to work permit.
'The Brazilian international flew to the UK and completed his medical earlier in the week, finalising a loan move which will automatically become a permanent deal until 2027, should certain clauses be triggered.'
Speaking to the club's official website, Cunha said: "I'm really excited to be part of this group and to be part of this club – it's a big club.
'I'm excited to play in the Premier League, to play in Wolverhampton, and I think the most important point is that I'm happy like a kid.
On being attracted to working under Lopetegui, Cunha added: "I know him as we've played against each other three or four times, and he's a big coach, he has a big mentality.
"He told me about him joining Wolverhampton and Wolverhampton having a big project and I took to the project, I believe in it a lot, and I believe in him. I also believe in the players, and I believe in the club."
Cunha has won eight caps for the Brazil national team but was not included in their squad for the Qatar 2022 FIFA World Cup.
