Swift came through the youth ranks with the Blues but made only one Premier League appearance for the club in May 2014.
The 21-year-old was then loaned out to Rotherham and Swindon but had a breakthrough season with Brentford last term, making 27 Championship appearances and scoring seven times.
This attracted the attention of Reading who have now snapped up the midfielder on a three-year deal.
And speaking to local newspaper Get Reading, Swift has revealed he opted not to sign a new deal at Stamford Bridge because he wanted the opportunity to work with manager Stam.
“We had good interest already from Reading but when Japp came in from Ajax it was really appealing to me – he wants to play football the way I do,” Swift said.
“I met him and that made up my mind… he’s someone to learn from, someone who has been at the very top level.
“Obviously he didn’t play in the same position as me but I can definitely learn from him every day in training.
“As soon as I knew that I wasn’t going to sign for Chelsea, Brentford were one of the teams that came in to sign me.
“But I was playing on the left there last season. Obviously I enjoyed it but I didn’t want to just settle on that. I wanted to look everywhere else.
“So luckily I waited, then Jaap came in at Reading and it was all done and dusted.”