The Roma goalkeeper will fly to London, where he will thrash out the finer details of his deal with the club before completing a £3 million move.
The transfer has been coming for some time, after negotiations broke down between the Italian club and Fulham in January.
Without European football to look forward to at Roma, and without a guaranteed first team spot, Stekelenburg has been pushing for a move from Serie A and Martin Jol has welcomed him with open arms.
The Fulham boss has made no secret of his desire to bring a new goalkeeper to Craven Cottage with current number one, Mark Schwarzer, turning 41 within two months of the start of next season.
This is in spite of the Australian's resilient form, having just put an end to another consistent campaign. It will be a blow to him, and he will undoubtedly quit the club, but there will be plenty of offers on the table.
The veteran has already rejected a contract offer from the club - though he has actually refuted the idea that one was offered - and it would take a miraculous change of heart for him to sign on.
It brings to an end a superb five year stint in SW6 for Schwarzer, having held fort through our gloriously successful Hodgson era and further.
Stekelenburg comes with considerable pedigree, though, and is well capable of filling in Schwarzer's gloves.