A source close to the couple, who started dating in June after the 24-year-old beauty attended one of his concerts in London, told Us Weekly magazine: ''He's fallen in love. It's the real deal.''
Jennifer has reportedly had a crush on the British rocker, 37, since she was a teenager.
Another insider said: ''It's a fantasy come true.''
The duo were recently spotted enjoying a romantic date at the Chateau Marmont hotel in West Hollywood last Thursday (11.09.14).
An eyewitness said: ''They made out at the table.''
A source previously revealed that Chris - who has children Apple, 10, and Moses, eight, with Gwyneth - pulled out all of the stops to romance Jennifer and has been writing love songs for her.
The insider said: ''He writes her songs and loves taking her to private romantic spots. Chris is sweeping Jen off her feet. That's his thing.''