The skull was found in an area alongside Arizona State Route 64 overlooking the Grand Canyon.

The skull was described by paleontologists Samuel Paul Welles and Richard Estes in 1969 and attributed to a new genus and species of brachyopid called Hadrokkosaurus bradyi.

In 2000, paleontologists Anne Warren and Claudia Marsicano suggested that the lower jaw and skull represent two different species, as they were found over 160 kilometres (99 mi) apart and come from two animals of different size.

Warren and Marsicano conducted a phylogenetic analysis of many brachyopoids and found Vigilius to nest within the family Brachyopidae.

Brachyopoidea is normally divided into the families Brachyopidae and Chigutisauridae, but these families are not always considered closely related; in some studies, Chigutisauridae is placed in a group of mostly Mesozoic temnospondyls called Stereospondyli while Brachyopidae is classified within a group of temnospondyls called Dvinosauria, which includes Carboniferous and Permian taxa that are older than Vigilius.