In 1979 the type species Torvosaurus tanneri was named. T. tanneri was a large, heavily built, bipedal carnivore, that could grow to a length of about 10 m (32.8 ft). T. tanneri was among the largest carnivores of its time, together with Epanterias (which may have actually been a large individual of Allosaurus) and Saurophaganax. Specimens referred to Torvosaurus gurneyi were initially claimed to be up to eleven metres long, but later shown to be smaller. Based on bone morphology Torvosaurus is thought to have had short but very powerful arms.
The genus name Torvosaurus means "savage lizard", and is derived from the Latin word torvus meaning "savage" and the Greek word sauros (σαυρος) meaning "lizard". The specific name tanneri, is named after first counselor in the First Presidency of The Church of Jesus Christ of Latter-day Saints Nathan Eldon Tanner. Torvosaurus gurneyi is dedicated to the paleoartist James Gurney. Torvosaurus was described and named by Peter M. Galton and James A. Jensen in 1979 and the type species is Torvosaurus tanneri.
Fossilized remains of Torvosaurus have been found in North America and Portugal. In 1971, Vivian Jones, of Delta, Colorado, in the Calico Gulch Quarry in Moffat County, discovered a single gigantic thumb claw of a theropod. This was shown to James Alvin Jensen, a collector working for the Brigham Young University. In an effort to discover comparable fossils, Vivian's husband Daniel Eddie Jones directed Jensen to the Dry Mesa Quarry, where abundant gigantic theropod bones, together with Supersaurus remains, proved present in rocks of the Morrison Formation. From 1972 onwards the site was excavated by Jensen and Kenneth Stadtman. The genus and the type species T. tanneri were named and described in 1979 by Peter Malcolm Galton and Jensen. In 1985 Jensen could report a considerable amount of additional material, among it the first skull elements. The fossils from Colorado were further described by Brooks Britt in 1991.
The holotype BYU 2002 originally consisted of upper arm bones (humeri) and lower arm bones (radii and ulnae). The paratypes included some back bones, hip bones, and hand bones. When the material described in 1985 is added, the main missing elements are the shoulder girdle and the thighbone. The original thumb claw, specimen BYUVP 2020, was only provisionally referred as it had been found in a site 195 kilometres away from the Dry Mesa Quarry. The holotype and paratypes represented at least three individuals: two adults and a juvenile. In 1991 Britt concluded that there was no proof that the front limbs of the holotype were associated and chose the left humerus as the lectotype. Several single bones and teeth found in other American sites have been referred to Torvosaurus.
In 1992, fossils of a large theropod found at Como Bluff in Wyoming, were named by Robert T. Bakker e.a. as the species Edmarka rex. This is often considered a junior synonym of Torvosaurus. The same site has rendered comparable remains for which the nomen nudum Brontoraptor has been used.
In 2000, material from Portugal was referred to a Torvosaurus sp. by Octávio Mateus and Miguel Telles Antunes. In 2006 fossils from the Portuguese Lourinhã Formation were referred to Torvosaurus tanneri. In 2012 however, Matthew Carrano e.a. concluded that this material could not be more precisely determined than a Torvosaurus sp. In 2013 eggs and embryos were reported from Portugal, referred to Torvosaurus. The species from Portugal was named T. gurneyi in honour of James Gurney in 2014. It is the largest theropod known from Europe.