The Cubs signed Staumont to a minor-league contract Friday, Darren Wolfson of Channel 5 Saint Paul reports.
He will report to Triple-A Iowa for now, but the Cubs could call the reliever up later this month. Staumont posted a 3.70 ERA in 24.1 innings with the Twins this season, but he had just a 18:14 K:BB and had surrendered 10 runs over his last six appearances before being released.