The 24-year-old Francisco was competing with Todd Frazier to back up Scott Rolen. Francisco was signed by the Reds in 2004 and was out of minor league options.
Francisco has played 81 games in the majors. The lefty hitter has a career batting average of .284 with five home runs and 29 RBIs.
Hoover, a former Rome Brave, was drafted by Atlanta in 2008. The Reds will assign him to Triple-A Louisville.
Hoover split last season between Triple-A and Double-A as a starter and reliever. He was a combined 3-6 with a 2.64 ERA.