Team officials didn't release the terms of the deal, but SI.com said the contract was worth a total of $13.35 million.
Jackson came to Arizona along with right-handed pitcher Ian Kennedy as part of a three-team Dec. 9 trade involving the Detroit Tigers and New York Yankees. Pitchers Max Scherzer and Daniel Schlereth went from the Diamondbacks to the Tigers and outfielder Curtis Granderson was sent from Detroit to the Yankees.
Jackson, 26, was a key cog on the Tigers' rotation last year, posting a 13-9 record with a 3.62 ERA in 33 starts and making the all-star team. For his career, Jackson is 38-39 with a 4.66 ERA in 139 games (110 starts).