Parnell signed a minor-league contract with the White Sox on Monday, Ken Rosenthal of Fox Sports reports.
Parnell began the season in the Royals' organization, but he exercised his opt-out clause after failing to garner a call-up during the first two months of the season. He appeared 15 times with Kansas City's Triple-A affiliate, producing a 4.71 ERA and 1.57 WHIP. His control was lackluster at best (5.6 BB/9), so he'll likely act as an organizational depth piece unless he can improve his performance.