Jarvik was born at a farm in Utby Parish near Mariestad in northern Västergötland. He studied botany, zoology, geology, and paleontology at Uppsala University, where he took his licentiate's degree in 1937. In 1942, he completed his PhD with the dissertation "On the structure of the snout of Crossopterygians and lower Gnathostomes in general". He participated in the Greenland expedition of Gunnar Säve-Söderbergh in 1932 and was appointed assistant in the Department of Palaeozoology of the Swedish Museum of Natural History in Stockholm in 1937; he eventually succeeded Erik Stensiö as professor and head of the department in 1960, retiring in 1972.