Songwriters Thomas Leonard and Martin Harrington sued the singer last June, claiming his hit ballad had a similar structure to their song, Amazing.
A lawyer for the pair confirmed to the BBC the claim had now been settled.
Leonard and Harrington's track was released by former X Factor winner Matt Cardle in 2012.
On Friday, court papers were filed dismissing the case with prejudice, stipulating that a California federal court would enforce the terms of an agreement.
Richard Busch, who represented Harrington and Leonard would not comment on the settlement terms.
A representative for Sheeran has yet to respond to the BBC's request for comment.
The songwriters originally claimed the chorus of the two songs shared 39 identical notes, with similarities "instantly recognisable to the ordinary observer".
They submitted the chord structures for both tracks in court documents.
Mr Busch is the same lawyer who won a case for the family of the late soul singer Marvin Gaye.
He successfully sued Robin Thicke and Pharrell Williams for copyright infringement last year over their single Blurred Lines, winning a $7.4m (£5.1m) settlement.