The deal seemed likely to go through, with the Dutchman understood to be frustrated by player sales and a lack of funds at the Amsterdam outfit.
There was also speculation he may have to sell keeper Maarten Stekelenburg, striker Luis Suarez and defender Gregory van der Wiel this summer.
But question marks surfaced over Jol's deal with the Cottagers before it fell through, despite Fulham chief executive Alistair Mackintosh travelling to the Netherlands for negotiations with Ajax.
"The club (Ajax) and I share each other's concerns," said Jol, who signed a three-year deal when he joined last July and looks to have been convinced to stay after talks with chief executive Rik van den Boog.
"Everyone knows that Ajax have financial difficulties. But we all want to perform better than last season. The expectations at Ajax are always high.
"Marko Pantelic, Dennis Rommedahl, Kennedy Bakircioglu and Gabri have all left the club and we haven't added anyone yet.
"Also, there is the uncertainty about whether a few other key players will stay.
The chairman and CEO would also like to personally thank Ajax for their conduct throughout this very public process
"Last Thursday was the first time I heard of Fulham's interest and it gave me some tough days as it made me doubt."
Jol led Ajax to victory in their domestic cup last season and they also finished runners-up by one point in the Dutch Eredivisie, with ex-England boss Steve McClaren's FC Twente pipping them to the league title.
Jol added: "I came here last summer to be successful, build a good team and to have fun - those three things are what I am interested in achieving next season."
A statement from Fulham added: "Since Roy Hodgson indicated that he wanted to leave Fulham, a shortlist of potential managers was identified, and the club is committed to ensuring that the right candidate is brought on board to continue the club's progress, in the soonest timeframe possible.
"The chairman [Mohamed Al Fayed] and CEO would also like to personally thank Ajax for their conduct throughout this very public process.
"Ray Lewington will remain in charge of all first team matters as caretaker manager and the club would like to thank Ray, his backroom staff and all the players for their patience and professionalism ahead of the 2010/11 Premier League season."
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