The midfielder, 20, agreed to a five-year deal with the French champions.
He scored 13 league goals for Anderlecht last season to help them win the Belgian title.
"Monaco is a club with an ambitious project, recognised on the European stage, and which relies on young players," Tielemans said.
"I am very happy to be here. I will now do everything possible to progress here and repay the confidence the club have shown in me."
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Monaco have signed Belgium's young player of the year Youri Tielemans from Anderlecht for a reported 25m euros (£21.63m).