The famed bachelor, 49, and model girlfriend Elisabetta Canalis, 31, flew in a private jet from Milan to the Italian island on Wednesday, where they were welcomed by Casare Canalis, Elisabetta's father, reported People.
Besides touring the scenic hillsides and coastal views, Elisabetta's uncle hosted a family luncheon for Clooney.
The couple also joined Elisabetta's parents for a quiet dinner at one of the town's most charming restaurants.
The small town with a population of only 1,200 was star-struck by the A-list visitor.
Fans and neighbors of the Canalis' stopped "The American" star for autographs, photos, and even one picture with a baby.
"He looked rather awkward with the 7-month infant in his arms, but he posed politely and carefully handed the baby back," said one neighbor, reported People.
Clooney, who has publicly stated he will never marry again, has been dating Canalis since last summer.