Leif was the son of Erik the Red and his wife Thjodhild, and the grandson of Thorvaldr Ásvaldsson, and distant relative of Naddodd, who discovered Iceland. He was a Viking in the early days. His year of birth is most often given as c. 970 or c. 980. Though Leif's birthplace is not accounted for in the sagas, it is likely he was born in Iceland, where his parents met—probably somewhere on the edge of Breiðafjörður, and possibly at the farm Haukadal where Thjóðhild's family is said to have been based. Leif had two brothers, whose names were Thorsteinn and Thorvaldr, and a sister, Freydís.
Thorvald Asvaldsson was banished from Norway for manslaughter and went into exile in Iceland accompanied by young Erik. When Erik was himself banished from Iceland, he travelled further west to an area he named Greenland, where he established the first permanent settlement in 986. Tyrker, one of Erik's thralls, had been specially trusted to keep in charge of Erik's children, as Leif later referred to him as his "foster father".