Buxierophus is known from the type species, Buxierophus pouilloni, which is named after French geologist Jean-Marc Pouillon. The species is known only from the holotype (RH-D 20–03–99), a partial skull and articulated anterior postcranium. It was named by German paleontologist Ralf Werneburg and French paleontologists Antoine Logghe and Jean-Sébastien Steyer. The holotype was found at the Buxières-les-Mines locality in the Bourbon-l'Archambault Basin in Allier; this locality is an open coal mine that has produced extensive faunal and floral remains, including algae, stromatolites, palynomorphs, blattoid insects, elasmobranch sharks, acanthodians, palaeoniscoid actinopterygians, and other temnospondyl amphibians ('archegosaurid' stereospondylomorphs, branchiosaurids, and eryopids).[2][3][4][5][6][7][8]
Buxierophus pouilloni is diagnosed by a combination of postcranial features: dorsal midline series of osteoderms composed of two series of thin and unornamented osteoderms, some bearing conspicuous peaks dorsally; internal osteoderms with bi- or multi-lobed dorsal articulation surfaces; neural arches of the same length to that of the osteoderm.[1] The skull is more generic with many common features of dissorophids, being slightly longer than wide, with large, laterally facing orbits. Well-eveloped ridges are found in several parts of the skull. The interpterygoid vacuities are large on the palate, which is covered by a shagreen of denticles.