The 33-year-old Ludwick and the Reds have a mutual option for 2013. The outfielder batted .237 last season in 139 games with the Padres and Pirates, hitting 13 homers with 75 RBIs. Ludwick also has played for the Rangers, Indians and Cardinals.
The 31-year-old Francis has struggled since he missed the 2009 season because of shoulder surgery. Last season, he was 6-16 for Kansas City with a 4.82 ERA in 31 starts.
The Reds also designated right-handed reliever Carlos Fisher for assignment to the minors on Wednesday.