He enters spring training as the likely replacement for closer Craig Kimbrel, who was traded to Boston.
Rodney gets a $1.6 million salary this year, and the Padres have a $2 million option for 2017 with a $400,000 buyout.
He can earn $1.5 million in performance bonuses each year based on appearances: $500,000 each for 40, 50 and 60 games. And he can earn $3.5 million annually for games finished: $250,000 each for 20 and 30, and $500,000 for 40 and each additional five through 65. The 2017 option would escalate by any performance bonuses earned this year.
Also Thursday, the Padres hired Mark Rogow as head trainer. He replaces longtime trainer Todd Hutcheson, who was released earlier in the offseason. Rogow spent the previous five years as sports medicine program manager for the Navy SEALs. He has more than 20 years of experience as a trainer in the New York Mets and Pittsburgh Pirates organizations.