Though it was originally interpreted as an early therapsid, it is probably a member of Sphenacodontidae, the family of synapsids that includes Dimetrodon.

Eosyodon hudsoni was named by Everett C. Olson in 1962 on the basis of fragmentary material from the San Angelo Formation in Texas.

A femur, currently cataloged as FMNH UR 575, was designated the holotype, and skull fragments, partial ribs, and a few other bones were also assigned to the species.

Olson interpreted Eosyodon as a therapsid closely related to Syodon, and assigned both genera to the family Brithopodidae of the infraorder Eotheriodontia.

A. Hopson presented a reevaluation of Olson's eotheriodonts at the annual conference of the Society of Vertebrate Paleontology, and concluded that they were based on caseid and sphenacodontid pelycosaurs.