He missed the 2018 season while recovering from Tommy John surgery.
Hatch, 24, has spent the past two seasons pitching in Double-A. He is 12-16 with a 4.14 ERA in 47 starts since 2018.
In other moves, the Cubs will place right-handed reliever Pedro Strop on the 10-day injured list and are calling up right-hander Duane Underwood from Triple-A Iowa, according to multiple reports.