The Netherlands international joined Fulham from Roma last year, but endured a disappointing debut season in England.
The 31-year-old suffered a number of injuries and made only 19 Premier League appearances as Fulham suffered relegation.
And the former Ajax stopper has now sealed a temporary switch to Monaco, with the club's chief executive Vadim Vasilyev telling their official website: "We are happy to have another goalkeeper with such an international experience.
"He has played the final of the World cup 2010 with the Netherlands."
Stekelenburg added: "I am happy to be a part of the project of the club. I am going to give everything for my new colours."
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