Brachyrhinodon and its single species B. taylori originally described in 1910 by German paleontologistFriedrich von Huene based on three specimens found near Elgin, Scotland where a number of reptile fossils have been found. The species was later redescribed in 1989 based on 12 specimens, representing at least 10 individuals. The specimens are largely preserved as negative moulds within the sandstone, which meant that casts needed to be made for description.
Brachyrhinodon is considered to be a member of Eusphenodontia. Some studies have recovered it as closely related to Clevosaurus,placing both genera as part of the familyClevosauridae, with some studies finding B. taylori nested within Clevosaurus. Other studies have recovered Brachyrhinodon as unrelated to Clevosaurus.