"Ever since Kristen's affair last year, Robert has realised just how much his friends and family in Britain mean to him," femalefirst.co.uk quoted a source as saying.
"After spending more time here in recent months, Rob's decided he wants to split his time more between London and Los Angeles.
"He wants to put down roots in London and he's doing it with Kristen. He's told her that if she wants to make things work, she's going to have to accept that he wants to spend much more time in London," added the source.
The couple already have their heart set on one luxury Victorian house in South West London, which has an "LA feel" to it and is close to Pattinson's parents' home.
"It's on the market for millions. Unlike the others they saw, this is suited to their tastes and needs very little work. They both fell in love with the property as soon as they saw it," said the source.
"They decided to base themselves in Richmond, South West London, so Rob can be close to his parents' home in Barnes," the source said.
Stewart, 22, is said to be really excited about spending more time in Britain.