Nunes, 23, was one of the stars as Sporting won their first Portuguese title for 19 years in the 2020/21 season and he helped them reach the Champions League last 16 last season.
The Brazil-born midfielder was described by Manchester City manager Pep Guardiola as “one of the best players in the world” after Sporting’s run in the Champions League was ended by the English champions in March.
Nunes had been linked with a move to Liverpool, but he has instead joined Wolves’ array of Portuguese talent thanks to the club’s close connections with super agent Jorge Mendes.
The fee could rise a further five million euros in add-ons.
“I think the club itself (convinced me) and also I spoke to some of my team-mates because I play with them for the national team,” said Nunes on choosing Wolves over other big clubs around Europe.
“The coach (Bruno Lage) 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.”
Nunes will be free to make his debut in Saturday’s trip to Tottenham as Wolves look to recover from a slow start to the season.
Lage’s men have taken just one point from their opening two games against Leeds and Fulham.