Thinking Out Loud is one of the biggest songs of Sheeran's career. It spent more than two years in the UK singles chart, racking up 4.8 million sales in the UK, and won song of the year at the 2016 Grammy Awards.
Gaye's boudoir ballad, which was a number one hit in the US, was co-written with singer-songwriter Ed Townsend, who died in 2003.
Townsend's family first accused Sheeran and Wadge of copyright infringement in 2016, seeking $100m (£73m) in damages.
In court, Sheeran's team accepted that the two songs share a similar syncopated chord pattern.
However, they characterised the chords as the "building blocks" of pop music, which had been used in dozens of songs before and since Let's Get It On was recorded in 1973.
A New York jury ruled in Sheeran's favour in 2023, after which the star spoke about his decision to fight the case in court, rather than settle.
"I am not and will never allow myself to be a piggy bank for anyone to shake," he told reporters.
SAS, which was founded and run by investment banker David Pullman, also has a stake in Townsend's copyright, and sued Sheeran and Wadge separately in 2018.
After losing that case, SAS launched a series of appeals, including demands for a re-hearing, which was denied.
SAS was then left with the option of appealing to the Supreme Court, which it did in March.
But the court agreed with earlier findings that the chord progression and harmonic rhythms in Gaye's song are too commonplace to be legally protected.
"And no reasonable jury could find that the two songs, taken as a whole, are substantially similar in light of their dissimilar melodies and lyrics," Judge Michael Park wrote for the New York-based 2nd US Circuit Court of Appeals.