The person spoke Friday on the condition of anonymity because the deal was pending a physical. Several outlets had earlier reported the agreement.
The 6-foot-3, 250-pound Abreu could play first base or serve as the designated hitter. He batted .360 (9-for-25) with three home runs and nine RBIs at the World Baseball Classic last spring, and he defected over the summer.
Abreu joins a team that went 63-99 after finishing second in the AL Central. The White Sox batted .249 with just 148 homers, down from 211 the previous year.
With Adam Dunn and Abreu in the mix, there might not be room for Paul Konerko.