The Brewers had placed Stinson on waivers to clear a spot on the 40-man roster.
Stinson made his major league debut with the New York Mets in 2011, posting an ERA of 6.92 with seven walks and eight strikeouts over 14 appearances spanning 13 innings. He was then claimed off waivers by the Brewers last April.
Last season, Stinson appeared in six games -- including one start -- for the Brewers. The 25-year-old allowed only one run over 9 1/3 innings with five walks and three strikeouts.
Stinson spent a majority of the year with Milwaukee's Double-A affiliate, maintaining an ERA of 3.16 over 29 appearances -- including 24 starts. Over seven seasons in the minors, he owns a career ERA of 3.98 with a strikeout-to-walk ratio of 1.63.
Prior to being placed on waivers by the Brewers, Stinson appeared in 10 games for Milwaukee this spring. He allowed two earned runs over 12 innings with eight walks and five strikeouts.