Erik Andersson, as his original name was, was born in the village of Stensjö in Döderhult parish in Kalmar County; he later took his new surname from his place of origin and is occasionally referred to with both names (as Erik Andersson Stensiö or Erik A. Stensiö). He received his Ph.D. and a docentship in paleontology from Uppsala University in 1921 and became professor and keeper at the Zoopaleontological (later called the Paleozoological) department of the Swedish Museum of Natural History in Stockholm in 1923, a position he held until his retirement in 1959.
Stensiö specialized in the anatomy and evolution of "lower" vertebrates. His studies of placoderms showed them to be related to modern sharks (though, now, placoderms are considered to be the sister group of all jawed vertebrates, in addition to sharks). His first major work was Triassic fishes from Spitzbergen (part I: Vienna 1921; part II: Stockholm 1925) was based on material collected during his expeditions to Spitsbergen in 1912, 1913, 1915 and 1916. For his work, The Downtonian and Devonian Vertebrates of Spitzbergen, Part I, Stensiö was awarded the Daniel Giraud Elliot Medal from the National Academy of Sciences in 1926.
Stensiö was a member of the Royal Swedish Academy of Sciences from 1927 and was elected a Foreign Member of the Royal Society in 1946. He received the Wollaston Medal in 1953, and the Linnean Medal of the Linnean Society of London in 1957. He was awarded the Linnean Society of London's prestigious Darwin-Wallace Medal in 1958.
- Patterson, C. (1990). "Erik Helge Osvald Stensio. 2 October 1891-11 January 1984". Biographical Memoirs of Fellows of the Royal Society 35: 362. doi:10.1098/rsbm.1990.0017.
- "Daniel Giraud Elliot Medal". National Academy of Sciences. Retrieved 16 February 2011.
- Nordisk familjebok, 2nd ed., vol. 38 
- History of the Department of Palaeozoology of the Swedish Museum of Natural History