The fee was not disclosed, but Wolves stated it is a club record, with British media reporting it to be around £38 million.
The transfer fee would surpass the £35 million Wolves paid for forward Fabio Silva in 2020.
Nunes has signed a five-year contract with Wolves, with a one-year option.
He had his breakthrough in the 2020/21 season when he helped Sporting to a league and a Portuguese League Cup title.
Nunes played his first game for Portugal's national side in 2021 against Qatar and has eight games and one goal for the team.
“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,” chairman Jeff Shi said.
After a defeat and a draw in their first two games of the new Premier League season, Nunes will be a welcome addition to Bruno Lage’s squad ahead of the travel to face Tottenham Hotspur.