The 23-year-old had been contracted to Ligue 1 side Lille, but spent last season on loan with Belgian outfit Zulte Waregem.
Crystal Palace, Liverpool and Everton have all previously been linked with a move for the Frenchman, although it is French champions Monaco that have won the race to sign the in-demand midfielder.
"It is 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," Meite told Monaco's official website.
"The coach, [Leonardo] Jardim, has succeeded in giving the team a real collective identity. I cannot wait to start training, learning and developing under his orders. I will be doing my best to show the club management that they were right to give me my chance."