The White Sox will pay Morneau $1 million, as announced. They designated Mat Latos for assignment in a corresponding move.
The 35-year-old Morneau is recovering from elbow surgery that will keep him out through midseason.
Last year, Morneau hit .310/.363/.458 with three home runs and 15 RBIs in 182 plate appearances with the Rockies. The prior season, he won the National League batting title with a .319 average.
When he becomes healthy, the former AL MVP (2006) will be brought in to Chicago to help add to their offense, which has been struggling this season.
Latos, 28, signed a one-year, $3 million deal with the White Sox during the offseason, and he struggled to a 4.62 ERA in his first 11 starts, including a 7.25 ERA in his last seven outings.