The New York Post reported Rivera, 43, has decided to conclude a career in which he has produced an all-time record 608 saves.
Rivera tore a knee ligament last May while catching fly balls during batting practice prior to a game against Kansas City.
He missed the remainder of the 2012 season, but announced he would return for 2013 because he did not want an injury putting an end to his career.
Rivera has yet to pitch this spring, but is due to make his first appearance Saturday.
Prior to last season, Rivera had recorded at least 28 saves in 15 consecutive campaigns. He has been chosen to the American League All-Star team 12 times.
Rivera has played on five World Series winning teams. He has 42 post-season saves with a 0.70 ERA in 141 playoff innings.