Stekelenburg, who began his career at Ajax Amsterdam and played in the 2010 World Cup final in South Africa but missed out on this year's tournament in Brazil, had been on Fulham's books since joining them from AS Roma last year.
"We are happy to have another goalkeeper with so much international experience," Monaco vice-president Vadim Vasilyev told Monaco's website (www.asm-fc.com).
The 31-year-old Stekelenburg. who will vie with Danijel Subasic for a starting spot, added: "I am happy to be a part of the club's project... I am a technical goalkeeper, I like playing far out of my goal and helping the team".
Monaco were runners-up to Paris St Germain in Ligue 1 last season, while Fulham were relegated from the Premier League.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Writing by Rex Gowar; Editing by Ken Ferris)
