The 20-year-old turned down a new contract at Molineux at the beginning of the month and had one year left on his current deal – with Wolves holding another year in their favour.
Otasowie was attracted interest from both Wolfsburg and Anderlech before Belgian side Brugge offered £3.5million for him a couple of weeks ago.
Wolves took their time to consider the bid – believing their contract offer to Otasowie was fair – and decided this week to accept Brugge's offer.
The midfielder had his medical on Wednesday and the move has now been announced by the club.
Technical director Scott Sellars said: “This is a fantastic opportunity for Owen to further his career. Our academy brought a boy from London at 15 and really developed him to become a full international and play in Premier League, which shows the great work being done here.
“Our job is to develop players to fulfil their potential. If it’s to play in our first-team then great, but it is obviously very difficult to make the grade in the Premier League, so if it means we’ll develop them and sell them, that is an important part of our strategy as well.
“In this case we have worked hard to develop Owen as a player and a person, and we have turned a young prospect into a multi-million pound player, and that will only benefit the Wolves Academy and our other young players coming through.”
Otasowie has been with Wolves since 2017 when he joined their academy. He made his senior Wolves debut in December 2019, coming off the bench against Besiktas in the Europa League, before signing a new contract with the club in January 2020.
He had to wait until December 2020 for his Premier League debut and impressed in a handful of games that followed, but his opportunities were limited under former boss Nuno Espirito Santo.
After suffering a hamstring injury during pre-season his game minutes were again limited.