Kasami joined from Serie A side Palermo on Monday and penned a four-year deal that will keep him at Craven Cottage until 2015.
The 19-year-old broke into the Italian outfit's first-team last season and emerged as one of the brightest talents in the league, leading to a host of clubs from across European considering a move this summer.
Jol, speaking at Stadion Hrvatski Vitezovi ahead of Thursday's third qualifying round clash with RNK Split, admitted he was delighted with the signing and to have beaten other clubs to get the player.
"Not everybody in England will know [how highly thought of he he is]," he said.
"He is a great talent and there were a few other clubs - big clubs as well - after him. It was nice to snatch him from other clubs' grasp.
"He is 19 but, on the other hand, he played more than 20 matches for Palermo in Serie A.
"He was probably the youngest player there that played so many games so I think he can play in our team now. He will play a big part this season."
Despite only joining the west Londoners on Monday, the Dutchman admitted Kasami could play a part in Thursday's first leg in Croatia if the club can sort out the paperwork.
"He has travelled," he said. "There is a little thing with the list that you can add one player so hopefully we can do that tonight.
"If not, he will not be involved. If he can do, he will be involved."
The Switzerland Under-21 international could be handed his first Fulham start alongside fellow debutant Marcel Gecov, who joined the club from Slovan Liberec last week before the second round tie with Crusaders.
While Kasami and Gecov come into the Fulham squad, David Stockdale will not feature after completing his loan move to npower Championship outfit Ipswich.
The former Darlington goalkeeper has been linked with several clubs over the summer and Jol admitted it was good to finalise the deal.
"I am happy the Stockdale situation has been concluded," he said. "Getting the clause inserted was the only matter so we can recall him if necessary."
Summer signing Csaba Somogyi will replace Stockdale as Mark Schwarzer's backup and will be part of the squad on Thursday.
However, Clint Dempsey and Mousa Dembele did not travel with Fulham to the Adriatic coast.
Their opponents RNK Split are relatively unknown outside their homeland but have enjoyed a meteoric rise in recent years.
The Reds have risen from the fourth tier to finish last season third in the Croatian top flight and Jol appreciates the home side will be keen to cause an upset against the Barclays Premier League side.
"Of course they will see it as a chance to put themselves on the map but it was probably the case at Crusaders as well and in the Faroe Islands," he said.
"They didn't want to lose because it was the biggest game in their history.
"If you can play against a Premier League club that will be the case.
"It is quite a story and they are of course in the top tier now.
"Dinamo Zagreb are probably the best side over here and Hajduk Split are very good club.
"It is a very good story but we have to win all these games."