The Twins released Webb on March 24.
Webb signed a minor-league contract Thursday with the Twins.
Webb elected free agency Friday, Jeff Jones of the Belleville News-Democrat reports.
The Cardinals assigned Webb to Triple-A Memphis after he cleared waivers Sunday.
Webb was designated for assignment by the Cardinals on Thursday.
Webb secured his second hold in a win over the Diamondbacks on Saturday, firing a scoreless eighth inning during which he allowed a hit and recorded a strikeout.
Webb, who allowed an earned run on two walks over 1.1 innings in a loss to the Padres on Friday, owns a 19.29 ERA over four May appearances.
Webb has allowed seven earned runs on four hits and seven walks while recording one strikeout across the 2.1 innings covering his last four appearances.
Webb, who fired a scoreless two-thirds of an inning in which he recorded a strikeout during Sunday's loss to the Brewers, has a 12.46 ERA and 1.38 WHIP across his first six appearances.
Webb owns a 3.86 ERA, 0.86 WHIP, 5:1 K:BB and three holds across the 4.2 innings covering his first five Grapefruit League appearances.