The 45-year-old succeeds fellow Portuguese Nuno Espirito Santo, who left Wolves at the end of the season after four years at Molineux.
"I'm happy, excited, with a big ambition to do great things for this club," said Lage.
Nuno, who took charge at Wolves in 2017, won the Championship in his first season before guiding the club to back-to-back seventh-placed finishes in the Premier League.
More to follow.