The couple met this month at Paris Fashion Week and instantly connected, the newspaper said.
"Kristen's not over Rob, but she's getting there and Michael's helping her through it," a source told The Sun. "She vowed to throw herself into work and be single this summer. But when she met Michael last week, they hit it off. They both hate the spotlight and are smart, bookworm types."
Stewart and Pattinson, who co-starred in four "Twilight" vampire blockbusters, broke up in May after three years of dating.
The two hit a rocky patch last July when Stewart was caught in a cheating scandal with her married "Snow White and the Huntsman" director Rupert Sanders.
Stewart and Pattinson separated for two months, during which Stewart wrote an open-letter apology to the actor and professed her love for him publicly for the first time. They then reconciled before breaking up this past May.
Pitt is best known for his work on TV's "Boardwalk Empire."