The 23-year-old, who spent last season on loan at Belgian club Zulte Waregem, has agreed a five-year deal starting on July 1.
Meite helped Zulte Waregem lift the Belgian Cup at the end of the campaign and is looking forward to the prospect of playing for the defending French champions.
He told Monaco’s website: “It’s an honour to sign for this great club. There are very good working facilities here.
“I followed the team’s results last year. The team has solidarity, technique and lots of pace.
“I can’t wait to start training, learning and developing under coach Leonardo Jardim’s orders. I’ll be doing my best to show the club management that they were right to give me my chance.”