Stekelenburg, 30, worked with Fulham manager Martin Jol at Ajax, where he began his senior career and won two Dutch titles. He joined Roma in 2011.
"Maarten Stekelenburg is a fine quality goalkeeper who I know well from my time working with him at Ajax and of course as the Dutch international goalkeeper I have always had an additional interest in his career," Jol said on Fulham's website.
"He is a player of great quality and technical ability whose distribution and ability to react quickly and read the game is exceptional; he will be a fantastic addition to the talented team of keepers that we already have."
Stekelenburg, who has signed a four-year deal at Craven Cottage, is a replacement for out-of-contract Australian Mark Schwarzer who is set to leave the club.
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