Cincinnati picked up the 32-year-old Wells on July 7 after his release from Washington. He was promoted from Triple-A Louisville on July 31.
Wells became a fill-in starter late in the season and was 2-1 with a 3.65 ERA in four September starts.
In his career with the White Sox, Pirates, Rangers, Cardinals, Rockies, Royals, Nationals and Reds, Wells is 67-99 with a 4.71 ERA.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.