The chorus of Taylor's new single Look What You Made Me Do follows the same rhythmic pattern as I'm Too Sexy.
After the song was released overnight, the duo tweeted: "Thank you Taylor Swift, what a marvellous reinvention!"
The group's spokesman confirmed to the BBC they were approached by Taylor's team in advance of the release.
Right Said Fred have been credited as writers on Taylor Swift's new single in one of the most bizarre musical combinations of the year.