[3] The holotype is MNHN AC 8746, a quarter of a skull and other associated postcranial remains, while other fragmentary specimens are known.

Teleosaurus was briefly noted on by Jean Vincent Félix Lamouroux in 1820 as Crocodilus cadomensis and then he sent the specimen to Georges Cuvier.

T. geoffroyi, described on the basis of now destroyed mandibular fragments, was considered a valid species by Vignaud (1995),[17] but it was made a probable synonym of T. cadomensis in 2020.

Its forelimbs were remarkably short, and would probably have been held close to the body when swimming to improve the animal's streamlining.

Unlike modern crocodilians, it lived in the open ocean, and it probably caught fish and squid with its sharp, needle-like teeth.