The Shadow Out of Time

 was one of H. P. Lovecraft's stories.

It described a parasitic, "eternal" alien race who had the ability to fling their essence through time and slowly take over the bodies of other races from the inside. A direct book described them as:

While he was working on the manuscript, which was illustrated by hand with eldritch symbols and drawings of the aliens, Lovecraft found himself flung forwards in time to by a mysterious orb. After getting glimpses of many eldritch beings, including the very race he had described in the book, he found himself emerging in 2023 London, where, acting on a Guardian of the Gate gut instinct, he gave the manuscript to Giles so that he and P.R.O.B.E. could deal with the threat of the "eternal race". (AUDIO: Guardian At The Gate)

Behind the scenes
The quote read by Giles is an actual quote from the 1936 real-world novella, although "at the end of two of their four limbs" is simplified to "at the end of their four limbs", a discrepancy presumably accounted for by the version quoted in Guardian At The Gate explicitly being a handwritten first draft, rather than the published version.