During the romantic break, 31-year-old Stacy tweeted: "I'm in heaven."
Sources say George and Stacy were introduced by mutual friends and while they are having fun together, neither is looking for a big commitment.
One told Life & Style magazine: "They have a lot of friends in common and run in the same circles.
"He's enjoying spending time with Stacy, but he just got out of a two-year relationship. George isn't ready for anything serious. This fling is purely for fun."
George, 50, is one of Hollywood's most famous bachelors and recently blamed his work commitments as the reasons why his relationships don't work.
George - whose previous girlfriends have included model Lisa Snowdon and waitress Sarah Larson – said: "I love working. I love being on a film set, trying to make something special. It is a very selfish life.
"It means my relationships seem to last between two and three years. At that point, these independent women think it is time to call it a day. They see me travelling round, putting work first, writing, directing, acting. It seems I never stop.
"I don't blame them for wanting more from a relationship."