The couple fell in love with a two-year-old golden retriever called Ren at a Los Angeles rescue shelter and decided to bring her home, reported People magazine.
"She was one of the dogs they first saw, but they weren't sure. They left and they couldn't stop thinking about her, so they came back for her. And it's true love," said a source.
The couple officially adopted the purebred pet on Christmas Eve after they initially brought her home last Saturday on a trial basis.
The British actor, 29, was spotted walking Ren for the first time on Monday and the source said he and 'Easy A' star Stone, 24, are already besotted with her.
"She won the doggie lottery. They totally fell in love with her," the source added.
Stone already has a small black and white dog of her own but this is believed to be their first pet together.
