The ex-Swansea assistant replaces Nuno Espirito Santo, who left Molineux at the end of the season.
Wolves targeted Lage, a free agent, as they look to change direction following Nuno’s four years in charge.
The 45-year-old initially failed to get through post-Brexit regulations but, at a hearing earlier this month, Wolves won their case and he was given the green light to move to the midlands club.
“First of all, I’m very happy,” Lage told the club’s website. “It’s a big opportunity. I’m very happy because I’ve returned to this country, and to be the manager of a big team.
“It’s a team and a club that wants to do history and a chance to compete in the Premier League. So, I’m happy, excited, with a big ambition to do great things for this club.”
Lage won the Portuguese title with Benfica in 2019 – also claiming manager of the year – before departing in 2020 after failing to defend their crown, finishing second behind Porto.
A move to Molineux marks a return to English football after Lage spent time as Carlos Carvalhal’s assistant at Sheffield Wednesday and Swansea.
“I was here (in the UK) for three years, so I know Wolves, but now, the best thing to do – the next thing to do – is to know everyone better,” Lage added.
“That includes the club, the fans, and also to try to create a plan, just not for the next game or the next training, but for the future.
“That’s why for me, it’s very important to create that dynamic of teamwork here in this building; to try to realise what we are doing in the future.”
Nuno left Wolves last month having taken them from the Sky Bet Championship to the Europa League quarter-finals.
He secured successive seventh-place finishes in the Premier League after promotion in 2018 but Wolves could only manage 13th in the 2020-21 campaign.
While his departure was officially by mutual consent, owners Fosun initiated the move as they looked to the club’s long-term future.
