Roma's sporting director Franco Baldini revealed earlier this week that the Italian side had reached an agreement with the Cottagers over the transfer of the Netherlands international.
It is reported that Fulham boss Martin Jol will pay in the region of £4million for the 30-year-old, who was close to signing for the club back in January.
Stekelenburg's agent, Rob Jansen, has now released a statement on his official website confirming a deal has been struck between the two clubs and the player is now discussing terms.
"The current employer of the goalkeeper, AS Roma, and Fulham have already reached an agreement on the transfer of Stekelenburg to London," read the statement. "Now the club and the player can see it out."