The 31-year-old former Ajax stopper had a disappointing season at Craven Cottage last term after arriving from Roma and was unable to prevent the London club's relegation.
He will compete with Croatia goalkeeper Danijel Subasic for the number one spot at Monaco.
Stekelenburg, who missed out on selection for Holland's 2014 World Cup squad, said on club website www.asm-fc.com: "I am happy to be a part of the project of the club.
"I am fully going to give myself for my new colours. I am a 'technical' goalkeeper. I like playing far from my goals and helping the team."
Monaco vice-president Vadim Vasilyev was pleased to have bolstered his club's goalkeeping options, having been heavily linked with Victor Valdes earlier this summer only to withdraw their interest in the former Barcelona man over medical concerns.
He said: "We are happy to have an other goalkeeper with such an international experience. He played in the final of the 2010 World Cup with the Netherlands."
- Sports & Recreation