Jarvik was born at a farm in Utby in 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.
Jarvik proposed partly controversial hypotheses about the principal structure of the vertebrate head and the origin of the tetrapods. He thus held, on the basis of detailed analyses of the snout and nasal capsule structures as well as the intermandibular, neuroepiphysial, and occipital regions, that urodeles (salamanders) were descended directly from primitive porolepiform fishes, while all other tetrapods (“eutetrapods”) – apodans possibly excepted – were descended from primitive osteolepiforms. This view was never widely accepted and is not held by vertebrate paleontologists today.
Jarvik also studied the anatomy and relationships of lungfish which he held to be relatively primitive gnathostomes, possibly related to holocephalans, and of acanthodians, which he considered to be elasmobranchs rather than osteichthyans. He made contributions to a number of classical problems in comparative anatomy, including the origin of the vertebrates the origin of the pectoral and pelvic girdles and paired fins, and the homologies of the frontal and parietal bones in fishes and tetrapods
Finally, Jarvik investigated the anatomy of Ichthyostega, resulting in a monograph with an extensive photographic documentation of the material collected in 1929-1955.
Some of Jarvik’s views did not accord with general opinion in vertebrate paleontology. However, his anatomical studies of Eusthenopteron foordi laid the foundations for modern studies of the transition from fishes to tetrapods. Jarvik was a member of the Royal Swedish Academy of Sciences and French Academy of Sciences and Knight of the Order of Vasa. The lungfish Jarvikia and the osteolepiform Jarvikina are named after him.