Acentrophryne longidens was first formally described in 1926 by the English ichthyologist Charles Tate Regan with its type locality given as 7°30'N, 79°19'W in the Gulf of Panama from a depth of around 1,250 m (4,100 ft), the holotype being collected by the Danish research vessel Dana.

This genus is known from the fossil record, as a single specimen was found in 1977 from a Miocene diatomaceous deposit in the Puente Hills of Southern California.

This was initially tentatively identified as being 'this species but its identity is now left open as Acentrophryne sp.

Its use may date as far back as Aristotle and Cicero, who referred to anglerfishes as "fishing-frogs" and "sea-frogs", respectively, possibly because of their resemblance to frogs and toads.

[7] Acentrophryne longidens is known from two specimens which were collected from two separate localities in the Eastern Pacific Ocean, in the Gulf of Panama and south of Cabo Blanco in Costa Rica.