The Netherlands international has penned a four-year deal following a switch from Roma.
The 30-year-old becomes the third major signing of the transfer window following the arrivals of defender Fernando Amorebieta and midfielder Derek Boateng.
"I am very happy to be joining Fulham, and to have everything sorted out so early in the summer, so I can really focus on preparations for playing in the Premier League next season," Stekelenburg told the club's official website.
"It’s good that I’ll be joining Martin [Jol] again, he knows my capabilities very well, so I am just looking forward to joining up with the team in pre-season and enjoying some time with them prior to the new season starting."
Manager Martin Jol expressed his delight at finally securing the Netherlands international's signature.
Jol added: "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. I am sure that he will do well here at Fulham in the Premier League.
"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."