The team announced the moves Wednesday. Pitchers and catchers report to camp on Feb. 14 in Surprise, Ariz.
The 35-year-old Penny, whose best years came with the Los Angeles Dodgers, is trying to resurrect his career after missing last season to rest his pitching shoulder. Penny was 0-1 with a 6.11 ERA in 2012 with the San Francisco Giants.
Mota has been with seven clubs, most recently the Giants. The right-hander is 39-45 with a 3.94 ERA over 14 seasons. He is coming off a 100-game suspension for a second positive drug test. His agent says it was for clenbuterol found in children's cough syrup.
The Royals also agreed to terms Thursday with left-hander Tim Collins on a one-year contract to avoid arbitration. Collins will make $1,362,500 this season, a substantial increase from the $534,500 he earned last season, when he was 3-6 with a 3.54 ERA in 66 appearances.
Information from The Associated Press was used in this report.