Samardzija, who can become a free agent after the 2015 season, signed his one-year deal for $9.8 million. Flowers agreed to a $2.675 million deal.
Samardzija, 29, is expected to be the No. 2 starter in the White Sox rotation behind Chris Sale. He went a combined 7-13 with the Chicago Cubs and Oakland Athletics last season, posting a 2.99 ERA while striking out 202.
Flowers batted .241 with 15 home runs and 50 RBIs in 2014. His 1,052 innings behind the plate last season were fourth-most in the American League and eighth-most in baseball.
The White Sox already agreed to deals with four other arbitration-eligible players this week: Dayan Viciedo ($4.4 million), Javy Guerra ($937,500), Nate Jones ($660,000) and Hector Noesi ($1.95 million).