The 'Say You Won't Let Go' hitmaker was hit by a legal claim over his 2016 single, which the band argued was similar to their 2008 track 'The Man Who Can't Be Moved'.
As reported by the Daily Mirror newspaper, the group's members Danny O'Donoghue and Mark Sheehan are now formally listed as songwriters on Arthur's song.
However, the terms of the settlement are not known.
The lawsuit - which was filed in 2018 and handled by their lawyer Richard Busch - claimed the song made James £14 million.
They demanded "all streaming, distribution, publishing and touring revenue connected to the song", plus statutory damages.
According to the publication, the lawsuit was settled in December 2018, but only now has the news come to light.
The 33-year-old star - who rose to fame after winning 'The X Factor' in 2012 - addressed the controversy in a freestyle rap on BBC Radio 1's 'Live Lounge' three years ago.
He branded The Script "snakes full of jealousy", and rapped: "Did you see – those desperate men call for desperate times? But they will never see a single flipping dime of mine.
"I’m dynamite; every single line I write, inspired by life. You can get your lawyers to indict me. You rich fellows that jealous you would spite me."
He had also hit out at supposed similarities between the two tracks the previous year, saying: "It's 2017, there's only seven notes in music.
"Every blues song sounds the f****** same. People get wound up about these things for no reason."
He said: "The thing about these things is everyone gets into a ‘he said, she said’ thing, and we don’t want to put James down.
"I don’t want anyone to put us down, so you’ve got to protect everybody’s career. We think James is a fantastic artist."
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