Led Zeppelin's Jimmy Page and Robert Plant said the origins of Stairway To Heaven had been put "to rest" after a jury found they did not plagiarise the song's famous guitar intro.
The veteran rock stars were accused of "lifting" the opening guitar section of their 1971 hit - one of the world's most recognisable rock songs - from an instrumental track called Taurus by the American band Spirit.
A lawsuit was filed by Michael Skidmore, the trustee of Spirit guitarist Randy Wolfe - known as Randy California - who drowned in 1997 having never taken legal action over the song.
Following a week-long trial in Los Angeles, a jury found that Taurus and Stairway To Heaven were not "extrinsically similar".
Lawyers for Mr Wolfe's trust had asked for him to be given a third credit for Stairway To Heaven, which has earned millions of pounds since it featured on the album Led Zeppelin IV.
In a joint statement following the verdict, Page and Plant said: "We are grateful for the jury's conscientious service and pleased that it has ruled in our favour, putting to rest questions about the origins of Stairway To Heaven and confirming what we have known for 45 years. We appreciate our fans' support and look forward to putting this legal matter behind us."
During the trial, guitarist Page said he owned five Spirit albums but he had never watched the band play live, and Taurus was "totally alien" to him.
He said he first heard the 1968 song when his son-in-law showed him a comparison with Stairway To Heaven on the internet a few years ago.
"I knew I had never heard it before. Something like that would have stuck in my mind," Page told the court. "I was a bit confused because I thought, 'What has this got to do with Stairway To Heaven?'."
Page, 72, said he wrote the music for Stairway To Heaven at Headley Grange manor house in Hampshire, as the earliest surviving recording of the song was played to the court.
Denying claims that he copied Taurus, Page compared Stairway To Heaven with Chim Chim Cher-ee from the Disney film Mary Poppins, because they both had a chord sequence that has "been around forever".
In his evidence, singer Plant, 67, said he had no memory of watching Spirit in Birmingham in 1970, because he was involved in a car crash that night.
The three surviving members of Led Zeppelin were briefly reunited during the trial when bassist John Paul Jones gave evidence. Jones - who was not a defendant in the case - said he could not recall seeing Spirit live and denied owning any of their albums or singles.
The court heard that Page and Plant had earned 58.5 million dollars (£40 million) from Stairway To Heaven and other Led Zeppelin songs over the past five years.
Music experts contested whether Stairway To Heaven and Taurus were "substantially similar" after the jury was told both songs feature a "descending chromatic chord progression" in A minor.
Musicologist Alexander Stewart said the rhythm, chords and harmonies of Taurus, and the introduction to Stairway To Heaven, were "virtually identical", while professional musician Kevin Hanson said the two songs had a "striking similarity".
But Lawrence Ferrara, a music professor at New York University, said a descending chromatic chord progression was a "musical building block" for a song and it can be found in music dating back 300 years.
The opening of Michelle by The Beatles, Johnny Mathis's 1960 hit My Funny Valentine and the 1967 song Music To Watch Girls By could all be compared with Taurus, he said.
After the verdict, Mr Skidmore's lawyer Francis Malofiy said he was "disappointed" with the jury's ruling and "justice wasn't served".
"There are obviously issues that can be appealed," he said.
Mr Malofiy said the lawsuit had been brought 45 years after the release of Stairway To Heaven because of a change in the law in 2014.
Speaking outside court, Mr Skidmore said: "Money has triumphed over common sense."
Neither Plant nor Page were seen leaving court following the verdict.
Wolfe - who was nicknamed Randy California by his friend Jimi Hendrix - drowned in 1997 saving his son off the coast of Hawaii.