The band, one of the best-selling rock acts of all time, was handed victory after the US Supreme Court declined to take up the case, meaning that a March 2020 decision by a US appeals court in Led Zeppelin's favor will stand.
Lead singer Robert Plant and guitarist Jimmy Page had been accused in the six-year long case of lifting the riff - one of the best-known openings in rock music - from a song called "Taurus," written by the late Randy Wolfe of the US band Spirit.
Wolfe, who performed as Randy California, drowned in 1997, and the case was brought by a trustee for his estate. It has been one of the music industry's most closely watched copyright cases, potentially exposing Plant and Page to millions of dollars in damages.
Led Zeppelin was the opening act for Spirit on a US tour in 1968, but Page testified in a 2016 jury trial in Los Angeles that he had not heard "Taurus" until recently.
The Los Angeles jury found the riff they were accused of stealing was not intrinsically similar to the opening chords of "Stairway to Heaven."Lawyers for Wolfe's estate and for Led Zeppelin could not immediately be reached for comment on Monday.