The Brewers selected Thomas with the 13th pick in the Rule 5 draft Wednesday, JJ Cooper of Baseball America reports.
The Cardinals outrighted Thomas to Triple-A Memphis on Thursday, Jeff Jones of the Belleville News-Democrat reports.
Thomas was designated for assignment by the Cardinals on Tuesday.
Triple-A Memphis reinstated Thomas (undisclosed) from its 7-day injured list Wednesday.
Triple-A Memphis placed Thomas on its 7-day injured list June 6 due to an unspecified injury.
St. Louis optioned Thomas to Triple-A Memphis on Thursday, Derrick Goold of the St. Louis Post-Dispatch reports.