The couple have reportedly already viewed a house in Los Angeles, California which they want to rent together, reported Sun Online.
"Russell doesn't mess about. He's throwing himself into this new relationship as they've really hit it off," a source said.
The 37-year-old, whose divorce from singer Katy Perry was officially finalised last month, started dating Brewster soon after his split with Perry.
"It's been going on for a few weeks. He really likes her. She's cute. She is all over him and Russell loves it," the source added.