The righty will be in his first season with Arizona after he was acquired on Nov. 14 for Minor Leaguers Andrew Velazquez and Justin Williams.
Hellickson, 27, was 40-36 with a 3.78 ERA in his five-year career with Tampa Bay.
The D-backs have two remaining arbitration-eligible players: right-hander Addison Reed and outfielder Mark Trumbo.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.