Goal exclusively revealed earlier on Wednesday, the Dutch goalkeeper completed a medical at the club's Motspur Park headquarters before confirming the £4 million switch.
The 30-year-old becomes the third major signing of the transfer window following the arrivals of defender Fernando Amorebieta and midfielder Derek Boateng.
|6/1||Fulham are 6/1 with Coral to be relegated next season
"It’s good that I’ll be joining Martin 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."
As revealed by Goal in April, Fulham have been trailing Stekelenburg for a number of weeks, and 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.
"I am delighted that he was so keen to come to join us and am very happy with the way that the summer is shaping up in terms of our signings, so on the whole I’m ever so pleased."