Bellingham has scored 21 goals for Real since signing in the close season from Borussia Dortmund for 103 million euros
Kompany joined Anderlecht from Manchester City in 2019 as player-manager, and now takes over from Franky Vercauteren, who had been handling coaching duties, in a purely managerial role.
"I want to fully commit to my role as a coach and need 100% of my time and focus for it. That's why I'm quitting as a football player," said Kompany, who enjoyed a trophy-laden 11-year spell in England with City.
"Our ambition and our hunger remains the same. I want to stay with the club for at least four seasons and prove that Anderlecht can play a modern style of football, with results."
Kompany's first game in charge will come on Sunday as Anderlecht take on Mouscron.
As defender and skipper at City, Kompany won four Premier League titles, two FA Cups and four League Cups with City and is widely regarded as one of the club's greatest ever players.
After making his international debut as a 17-year-old, he went on to play 89 times for Belgium, notably leading them to third in the 2018 World Cup.
Bellingham has scored 21 goals for Real since signing in the close season from Borussia Dortmund for 103 million euros
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