The 34-year-old is so smitten with the 23-year-old British model-actress that he even invited her to his native Minneapolis last month for a friend's birthday party, reported Daily Star online.
"Josh doesn't usually bring his girlfriends home, so this one must be special. He's really into Tamsin," a source said
Hartnett split from "Mamma Mia" actress Amanda Seyfried in April because she was too busy filming "Les Miserables" in London while he was in New York.