The species was first described by the Danish zoologist Ferdinand Victor Alphons Prosch in 1849 as Cranchia megalops.
The type specimens were paralarvae obtained off the Faeroe Islands.
He included it under a new "subfamilia Cranchidæ" (now the family Cranchiidae), after noticing its similarity to Cranchia scabra and Cranchia maculata (now Teuthowenia maculata).
He further divided the group into two subgenera, placing the latter two under the subgenus Cranchia and separating Cranchia megalops into the subgenus Owenia (named after the British biologist Richard Owen).
The specific name was derived from Greek for "large eyes", from μέγας (megas, "great") and ὤψ (ops, "eye" or "face").

In 1850, the Danish malacologist Otto Andreas Lowson Mörch pointed out mistakes in Prosch's original description.
In 1856, the Danish zoologist Japetus Steenstrup mentioned a specimen of cranchiid squid recovered from Baffin Bay which he had named Leachia hyperborea.
Later in 1861, Steenstrup established the new genus Taonius, including Loligo pavo (now Taonius pavo) and his species Leachia hyperborea (as Taonius hyperboreus) within it.
In the same work, he was also the first to point out that Prosch had made the error of including juveniles of Gonatus along with his diagnosis of Cranchia megalops.
In 1879, the American malacologist George Washington Tryon included Teuthowenia megalops under the genus Cranchia, together with Teuthowenia maculata (then Cranchia maculata).
But he separated Steenstrup's Taonius hyperboreus to the genus Loligopsis along with Taonius pavo.

In 1881, the American zoologist Addison Emery Verrill established the genus Desmoteuthis for a new species he named Desmoteuthis tenera caught off New England.
He also recovered several specimens of Taonius pavo which he incorrectly identified as Taonius hyperboreus, leading him to also include Taonius hyperboreus under his new genus as Desmoteuthis hyperborea.
In 1884 and subsequently in 1886, the British zoologist William Evans Hoyle recognized Verrill's mistake after examining Verrill's well-illustrated paper.
He synonymized Verrill's genus Desmoteuthis back to Steenstrup's Taonius.
He also tentatively identified Verrill's Desmoteuthis tenera as a possible synonym of Taonius hyperboreus.
In 1884, the German zoologist Georg Johann Pfeffer established the genus Megalocranchia, using the type species Megalocranchia maxima.
Though the type specimens were destroyed in World War II, examinations of his description and illustrations reveal that Megalocranchia maxima was definitely not from the genus Teuthowenia.
Despite this, Pfeffer synonymized Megalocranchia with Verrill's Desmoteuthis in 1900.
He mostly followed Hoyle's conclusions regarding Taonius pavo but retained the genus Desmoteuthis for Taonius hyperboreus.
He also raised the Prosch's subgenus Owenia to genus level, thus renaming Cranchia megalops to Owenia megalops.
However, the name Owenia was already preoccupied.
Thus in 1910, the German zoologist Carl Chun established the genus Teuthowenia in its place, from Greek τευθίς (teuthis, "squid") + Owen, as in the original name.
Chun also first described Desmoteuthis pellucida (now Teuthowenia pellucida) from the same work.

In 1912, the American zoologist Samuel Stillman Berry agreed with Hoyle in concluding that Verrill's Desmoteuthis is a synonym of Taonius.
But he made the mistake of using Pfeffer's Megalocranchia for Desmoteuthis hyperborea; and inexplicably established a new genus Verrilliteuthis for Desmoteuthis tenera (which had previously already been recognized as a synonym of Desmoteuthis hyperborea).
Pfeffer followed suit in the same year by resurrecting Megalocranchia in agreement with Berry, though he still retained Desmoteuthis hyperborea in Desmoteuthis.

In 1925, the German malacologist Eduard Degner first described the growth stages of Desmoteuthis hyperborea during the Danish Oceanographical Expeditions (1908–1910) to the Mediterranean Sea aboard the Danish research vessel Thor.
He also described a new species Desmoteuthis thori from a subadult female specimen
The species was first described by the Danish zoologist Ferdinand Victor Alphons Prosch in 1849 as Cranchia megalops. The type specimens were paralarvae obtained off the Faeroe Islands. He included it under a new "subfamilia Cranchidæ" (now the family Cranchiidae), after noticing its similarity to Cranchia scabra and Cranchia maculata (now Teuthowenia maculata). He further divided the group into two subgenera, placing the latter two under the subgenus Cranchia and separating Cranchia megalops into the subgenus Owenia (named after the British biologist Richard Owen). The specific name was derived from Greek for "large eyes", from μέγας (megas, "great") and ὤψ (ops, "eye" or "face").
In 1850, the Danish malacologist Otto Andreas Lowson Mörch pointed out mistakes in Prosch's original description. In 1856, the Danish zoologist Japetus Steenstrup mentioned a specimen of cranchiid squid recovered from Baffin Bay which he had named Leachia hyperborea. Later in 1861, Steenstrup established the new genus Taonius, including Loligo pavo (now Taonius pavo) and his species Leachia hyperborea (as Taonius hyperboreus) within it. In the same work, he was also the first to point out that Prosch had made the error of including juveniles of Gonatus along with his diagnosis of Cranchia megalops. In 1879, the American malacologist George Washington Tryon included Teuthowenia megalops under the genus Cranchia, together with Teuthowenia maculata (then Cranchia maculata). But he separated Steenstrup's Taonius hyperboreus to the genus Loligopsis along with Taonius pavo.
In 1881, the American zoologist Addison Emery Verrill established the genus Desmoteuthis for a new species he named Desmoteuthis tenera caught off New England. He also recovered several specimens of Taonius pavo which he incorrectly identified as Taonius hyperboreus, leading him to also include Taonius hyperboreus under his new genus as Desmoteuthis hyperborea. In 1884 and subsequently in 1886, the British zoologist William Evans Hoyle recognized Verrill's mistake after examining Verrill's well-illustrated paper. He synonymized Verrill's genus Desmoteuthis back to Steenstrup's Taonius. He also tentatively identified Verrill's Desmoteuthis tenera as a possible synonym of Taonius hyperboreus. In 1884, the German zoologist Georg Johann Pfeffer established the genus Megalocranchia, using the type species Megalocranchia maxima. Though the type specimens were destroyed in World War II, examinations of his description and illustrations reveal that Megalocranchia maxima was definitely not from the genus Teuthowenia. Despite this, Pfeffer synonymized Megalocranchia with Verrill's Desmoteuthis in 1900. He mostly followed Hoyle's conclusions regarding Taonius pavo but retained the genus Desmoteuthis for Taonius hyperboreus. He also raised the Prosch's subgenus Owenia to genus level, thus renaming Cranchia megalops to Owenia megalops. However, the name Owenia was already preoccupied. Thus in 1910, the German zoologist Carl Chun established the genus Teuthowenia in its place, from Greek τευθίς (teuthis, "squid") + Owen, as in the original name. Chun also first described Desmoteuthis pellucida (now Teuthowenia pellucida) from the same work.
In 1912, the American zoologist Samuel Stillman Berry agreed with Hoyle in concluding that Verrill's Desmoteuthis is a synonym of Taonius. But he made the mistake of using Pfeffer's Megalocranchia for Desmoteuthis hyperborea; and inexplicably established a new genus Verrilliteuthis for Desmoteuthis tenera (which had previously already been recognized as a synonym of Desmoteuthis hyperborea). Pfeffer followed suit in the same year by resurrecting Megalocranchia in agreement with Berry, though he still retained Desmoteuthis hyperborea in Desmoteuthis.
In 1925, the German malacologist Eduard Degner first described the growth stages of Desmoteuthis hyperborea during the Danish Oceanographical Expeditions (1908–1910) to the Mediterranean Sea aboard the Danish research vessel Thor. He also described a new species Desmoteuthis thori from a subadult female specimen
Teuthowenia megalops