Gillaspie had been sidelined with a bruised left hand. He played in three rehab games with Charlotte, going 2 for 12 with a home run.
The 27-year-old Danks was recalled from Charlotte on April 10. He was 4 for 41 (.098) with a home run and five RBIs in 21 games with the White Sox.
Gillaspie hit .302 with 12 RBIs in his first 16 games with the White Sox.
The White Sox announced the moves before Wednesday night's game against the Cubs.