Chicago also agreed to a $2,675,000, one-year deal with catcher Tyler Flowers on Friday, giving the White Sox contracts with all their arbitration-eligible players.
Samardzija, who turns 30 on Jan. 23, can become a free agent after this season.
He was 7-13 with a 2.99 ERA with the Chicago Cubs and Oakland last year. The White Sox acquired him from the Athletics at baseball's winter meetings in December, one of several big moves by a team eyeing a jump after two losing seasons. The White Sox also added reliever Zach Duke, closer David Robertson and first baseman Adam LaRoche.
Flowers, who turns 29 Jan. 24, hit .241 with 15 homers and 50 RBIs last season.
Samardzija made $5,345,000 last year and Flowers $950,000.