1892, in C.G. Chaddock's translation of Krafft-Ebing's "Psychopathia Sexualis," from German homosexual, homosexuale (by 1880, in Gustav Jäger), from Greek homos "same" (see homo- (1)) + Latin-based sexual.
'Homosexual' is a barbarously hybrid word, and I claim no responsibility for it. It is, however, convenient, and now widely used. 'Homogenic' has been suggested as a substitute. [H. Havelock Ellis, "Studies in Psychology," 1897]
Sexual inversion (1883, later simply inversion, by 1895) was an earlier clinical term for "homosexuality" in English, said by Ellis to have originated in Italian psychology writing. See also uranian. Unnatural love was used 18c.-19c. for homosexuality as well as pederasty and incest. Related: Homosexually.