Varela was born in Santiago, Chile, the daughter of Leonor, a massage therapist, and the famous Chilean biologist and cognitive neuroscientist Francisco Varela. She has one sister Alejandra and two brothers, Javier and Gabriel. Varela's family fled to Costa Rica in her early childhood when her homeland was overtaken by a military regime. She subsequently resided in Germany, the U.S., and France. In the early 1990s, her parents moved back to Chile, while she remained in Paris where she studied acting at the Neils Arestrup's School, The Ecole de Passage, and Conservatoire Superieur de Paris.