Trincao has made 43 appearances for Barca since joining from Braga for €31 million last year, scoring two goals and three assists.
The Portugal U-21 international has six senior caps, although he was not included his country's Euro 2020 squad. He joins a strong Portuguese contingent at Wolves, having played alongside six of his new teammates in the national side.
"We've watched him a lot, especially over the last couple of months, so he's been on our radar for quite a while," Wolves technical director Scott Sellars said in a statement.
"He's got loads of quality -- signing for Barcelona from Braga shows what potential he's got. He's 21 and has played quite a lot of games in La Liga, so we think he's ready for the Premier League."
Tirincao is the first signing under new Wolves manager Bruno Lage, who came in after Nuno Espirito Santo left at the end of last season before becoming the Tottenham boss on Wednesday.