Leonor Varela was born in Santiago, Chile, the daughter of Leonor Pilme-Keller, a massage therapist, and Chilean biologist and cognitive neuroscientist Francisco Varela García. Leonor Varela has a sister, Alejandra, and two brothers, Javier and Gabriel. Her mother was of French, Hungarian, and Syrian descent. When Varela was a child, her family fled Chile when it was overtaken by a military regime. In the early 1990s, Leonor Varela parents moved back to Chile while she remained in Paris where she studied acting at the Niels Arestrup School, L'École du Passage, and Conservatoire Supérieur de Paris.