Lage was previously Benfica boss during the 2019/20 season.
He takes over from Schmidt after the German's two-year reign was ended last weekend after a difficult start to the season which has left Benfica seventh in the Primeira Liga on seven points from four matches.
"I had a huge desire to come and work at this club where I feel at home," said Lage in a press conference.
Schmidt led Benfica to their first Portuguese league title in four years in 2023, but they finished 10 points adrift of champions Sporting Lisbon last season.
Portuguese Lage was most recently coach of Brazilian club Botafogo but was sacked after just 15 games at the helm last October.
He was Wolves' manager in the Premier League for the 2021/22 season, before being fired early in the following campaign.
