The former Girls Aloud star was hired as a judge for the first season of the Tv talent show in 2011 after previously sitting on the panel of the British version, but she was dropped and replaced by Nicole Scherzinger after filming just two audition rounds .
Cole subsequently sued executives at Blue Orbit Productions, the team behind the show, claiming she was owed around $2.3 million (£1.5 million) in unpaid wages and expenses, and the case has now been settled out of court.
Details of Cole's settlement have not been made public, but a spokesman for the star tells the Bbc, "Cheryl's dispute with Blue Orbit has been resolved amicably."
Cole exit from the Tv talent show led to a nasty rift between the singer and the show's creator, Simon Cowell, but the pair has since patched up its friendship. She detailed the dispute in her 2012 autobiography, Cheryl: My Story, writing, "Simon didn't even have the guts to phone or send a message warning me what was coming. I was furious... I believed we had a good friendship and I couldn't understand why he hadn't been straight with me."