The Hollywood Reporter said court papers were filed on Friday dismissing the case with prejudice, meaning permanently, but stipulating that a California federal court would retain jurisdiction to ensure the terms of an agreement were adhered to.
Harrington and Leonard, along with their publishing company HaloSongs, alleged that Photograph drew on a song they penned in 2009 which was recorded and released as a single by Matt Cardle, the winner of the 2010 series of The X Factor.
The lawsuit claimed that Amazing had been copied “verbatim” with “note for note copying,” the Hollywood Reporter said.
Their lawyer Richard Busch told Sky News: “I can confirm the case has settled but cannot comment further.”
Sheeran’s publicists at Atlantic Records and his lawyers are yet to respond to a request for comment from Sky News.
Sheeran also faces a lawsuit over allegations he copied the core elements of Marvin Gaye classic Let’s Get It On for his song Thinking Out Loud.
A previous lawsuit involving allegations Pharrell Williams and Robin Thicke’s hit Blurred Lines had been derived from Marvin Gaye’s 1977 hit Got To Give Up led to Gaye’s family winning £4.8m in damages.
Mr Busch represented the plaintiffs in the latter case.