Lecomte, 28, who was part of coach Didier Deschamps' most recent France squad in June but did not feature has played 194 Ligue 1 matches since his debut for former club Lorient.
According to sources the fee could rise to 13 million euros ($14.64 million) with different bonuses.
Following an injury to ex-Croatia keeper Danijel Subasic, Lecomte is expected to be Monaco manager Leonardo Jardim's number one for the coming season.
Lecomte is Jardim's second summer signing. Gelson Martins joined on a permanent deal after spending the last half of last season on loan from Atletico Madrid.
Monaco narrowly avoided relegation from Ligue 1 finishing two points above 18th-placed Dijon who won a play-off with Ligue 2's Lens to retain their top-flight status.