The couple recently started dating after meeting on the set of 'Wanderlust' last year and are so serious about each other that the actress is believed to have asked Justin - who has an apartment in New York and usually stays at the luxurious Chateau Marmont when he is in Hollywood - to move in to her Beverly Hills pad.
A source told UsMagazine.com: "He's living at her place in L.A.! And she's introducing him as her boyfriend."
One person sure to be unhappy with the news is Justin's former girlfriend Heidi Bivens - who is said to be "heartbroken" after he moved out of the home they share last weekend.
A representative for Heidi said: "Heidi and Justin have been together for 14 years. They met when she was 20 years old and he 24, and yes, she just moved out of their home last weekend. She has no comment."
Though the costume designer refused to be drawn on the reports, some of her pals say the news came as a shock.
A source told the New York Post newspaper: "Heidi is heartbroken. She was completely blindsided. She and Justin had been together for years, they had a home."
However, friends of Justin, 39, say his relationship with Heidi was over long before he met Jennifer, 42, last year.
A pal said: "Things were already over between him and Heidi before he got close to Jen."