The story was first reported by ESPN.
Choice confirmed the move on his Twitter page, writing, "I just want to say thanks to all the great dallas cowboy fans. My time in Dallas has come to an end and the best is yet come. God bless."
Choice, 26, is averaging 2.7 yards on 28 carries without any touchdowns this season. He will go on waivers because he has less than four seasons of tenure.
Choice started against the St. Louis Rams last week, but it was Murray who stole the show with a team-record 253 rushing yards.