Right back had a medical with the club on Friday ahead of a permanent move
Kelly had been a prominent member of the Fulham squad last season but, with the loan signing of full back, Sascha Riether, the Irishman has been out of favour.
Jol admitted that a lack of playing time was a key factor in letting the defender leave.
"I thought it was good for him because he wanted to play," said Jol.
"Last year he played all the games almost so I thought it was good for him to talk to Reading and they decided to take him and he decided to go there."
But Kelly will be January's first and only sale, if Jol gets his way.
"It's a permanent deal. We won't lose any other players. It's one single player who could go in this transfer window. Kelly is the only one."
Are you sad to see Kelly go?
Yes (7 votes)
No (5 votes)
Not overly fussed (7 votes)
19 total votes