Davidson was born in 1923 in Yonkers, New York. He served as a Navy hospital corpsman (medic) with the Marine Corps in the Pacific during World War II, and began his writing career as a Talmudic scholar around 1950. This made his study of and conversion to Tenrikyo in the 1970s rather surprising. Although he had a reputation for being quick to anger when anyone tampered with his work or misunderstood it, Davidson was also greatly in demand as a storyteller, and well-known among his friends for his extreme generosity.
He was a member of the Swordsmen and Sorcerers' Guild of America (SAGA), a loose-knit group of Heroic Fantasy authors founded in the 1960s, some of whose works were anthologized in Lin Carter's Flashing Swords! anthologies.
While editing The Magazine of Fantasy and Science Fiction he lived in Mexico, and later in British Honduras (now renamed Belize). He lived in a rural district of Novato, in northern Marin County, California, in 1970, but later moved closer to San Francisco. He lived in a small house in Sausalito, at the southern end of Marin County next to San Francisco in 1971 and 1972, and it was there fans and friends were affectionately welcomed. In his later years, he lived in Washington state, including a brief stay in the Veterans' Home in Bremerton. He died in his tiny apartment in Bremerton on May 8, 1993, aged 70. A memorial service was held in Gasworks Park in Seattle.
He was survived by his son Ethan and his ex-wife Grania Davis, who continues to edit and release his unpublished works.