Fulham manager Martin Jol worked with Stekelenburg while the two were at Ajax between 2009 and 2010.
"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."
Franco Baldini, the Serie A club's sporting director, revealed that a deal has been struck with the Cottagers for 30-year-old Stekelenburg.
"I went to London for the sale of Stekelenburg at Fulham," Baldini told Corriere dello Sport. "There were questions to be answered, but I closed a deal subject to the usual conditions."