Simon, who pitched for the Reds from 2012-14, is expected to be part of the starting rotation despite the mid-March signing.
Simon, 34, was an All-Star for Cincinnati in 2014 when he went 15-10 with a 3.44 ERA.
The Reds dealt him to the Detroit Tigers prior to last season and Simon experienced a sharp drop-off. He went 13-12 with a 5.05 ERA and was allowed to depart as a free agent.
Earlier this offseason, Simon reached a $150,000 settlement with a woman who alleged she was raped by the pitcher in 2013.
Simon has a 45-40 career record in 240 games (82 starts) since reaching the majors with the Baltimore Orioles in 2008.