The 20-year-old, who has already been capped at senior international level by France, started his career with Lens before making the move to Sevilla 12 months ago.
He continued to impress in Spain to attract the attention of several clubs this summer, and Sevilla admitted earlier this week that he would be buying out his contract to allow him to leave.
Monaco have now announced that Kondogbia has penned a deal until 2018, in another move which demonstrates the ambition of the French side.
Arsenal and Real Madrid had been among the other clubs linked with the powerful midfielder this summer.
Gunners manager Arsene Wenger has been frustrated in his attempts to add to his squad during the transfer window but has insisted there will be no panic buys before Monday's deadline.