Lage returns to England, having previously served as assistant to Carlos Carvalhal at both Sheffield Wednesday and Swansea City.
The 45-year-old had been out of work since leaving the Estadio da Luz last summer after 18-months in charge of Benfica, where he won one Portuguese league title.
Esperito-Santo stepped down as Wolves manager at the end of the season after four seasons in charge at Molineux. He joined Wolves in the summer of 2017 and guided them from the Championship to the Premier League in his first season at the club.
Wolves secured back-to-back seventh place finishes in their first two seasons in the Premier League under Esperito Santo and reached the quarterfinal stage of last year’s Europa League but they could only finish 13th in 2020/2021.
"First of all, I’m very happy. 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,” Lage told Wolves’ official website.
“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.”
“I want to create a good dynamic of group, with my staff, with all the departments of the club.”
“I have tried to link all together to start to build up the new cycle. I think it’s a good opportunity to understand what Nuno did in these four years and my ambition is to continue and to improve what he did.”