The deal was announced on Friday. Lindstrom will receive $2.3 million next season. The White Sox can then pay him $4 million in 2014 or buy him out for $500,000.
The 32-year-old right-hander was 1-0 with a 2.68 ERA and 40 strikeouts over 46 games with Baltimore and Arizona last season. He was traded to the Diamondbacks on Aug. 26 for left-handed pitcher Joe Saunders and a player to be named later.