The 19-year-old midfielder has long been linked with the Craven Cottage outfit and has now completed his move.
David has represented Holland at youth levels and was close to a move to Fulham in the summer.
"He is here," Jol said of David. "He has signed and he is here.
"He trained with us this morning. He is 19 years of age, player of the year of all the academies in Holland.
"He is an exciting talent but he will need at least six months of a year to adapt, but hopefully he will do it quicker. He is a very, very good talent.
"People say Ajax were interested and I imagine there will have been other clubs who were interested in him.
"We are very happy to get him. Maybe you can remember there was a little worry with his medical check on the last day of the transfer window so we decided not to do it.
"We took more time and that was a little problem for the boy because he couldn't play.
"First we have to get him fit and after that you will see he is an international player at all levels so I am very happy we have got him."
Meanwhile, Jol also confirmed former Middlesbrough midfielder Mickael Tavares is to leave the club after being brought in on a month-to-month basis in October.
"He was a great pro and I knew him from Hamburg, but he was a back-up player," the Dutchman said.
"There was no necessity to use him so we thank him for being here but we decided not to extend that contract. This was probably his last day."
The Dutchman was also asked about Roma goalkeeper Maarten Stekelenburg and Dnipro's Derek Boateng, who is reportedly seeking a work permit ahead of a move to west London.
"There is no latest," Jol said. "There is always speculation. We will only tell you hopefully in the next couple of weeks if something happens and nothing happened.
"There is a lot of talk in papers and media in England, although 95 percent of all these names that are mentioned are not true.
"We won't mention names, we won't speculate and we won't tell you until something happens."
Jol was speaking ahead of Saturday's FA Cup third-round tie with Blackpool at Craven Cottage.
Mahamadou Diarra, Mladen Petric, Mark Schwarzer and Damien Duff all miss out on the clash through injury, while Stephen Kelly and John Arne Riise are also unavailable.
However, Jol has pledged to name as strong a side as possible as he looks to progress in a competition close to his heart.
"I love the competition," he said. "When I played in England with West Brom it was always special.
"Most of the time, if not all the time, they were sell-outs and for a lot of teams a reason to spark up your season, to do something nice. That is what I always thought of the FA Cup."