The Brazilian-born Portugal international has joined for an initial £38m fee which could rise by a further £4m with add-ons.
Nunes has signed a five-year contract at the Molineux Stadium and becomes manager Bruno Lage's third summer signing following the earlier arrivals of Nathan Collins from Burnley and Goncalo Guedes from Valencia.
Wolves' previous transfer record was the £35m they paid FC Porto for striker Fabio Silva in 2020.
Nunes made 101 appearances in total for Sporting Lisbon and was part of the squad that won the Portuguese Primeira Liga in the 2020/2021 season.
He has won eight caps for the Portugal national team and is set to feature at the 2022 FIFA World Cup in Qatar.
Speaking to the club's official website, Nunes said: "I'm very excited. For me, I could play tomorrow already, but I can't because the game is Saturday, but I'm looking forward to it.
"I think the club itself [convinced him] and also I spoke to some of my teammates because I play with them for the national team. The coach as well, he really wanted me, and I wanted to play in the Premier League. I think it's the right next step for me and I'm very happy to be here."
Wolves chairman Jeff Shi added: 'We are very happy to welcome Matheus to Wolverhampton, and delighted to add another exciting young talent to Bruno’s squad.'
'Matheus has had two excellent seasons at the top level in Portugal with Sporting and is widely regarded as one of the most exciting prospects in world football, so we are thrilled that he has chosen the Premier League and Wolves as the next step in what we hope will be a fantastic career.'
Nunes is in line to make his Wolves debut against Tottenham Hotspurs this weekend.
