Weber was designated for assignment by the Brewers on Tuesday.
The Brewers claimed Weber after the right-hander was DFA'd by Boston last month. He pitched one scoreless inning for Milwaukee before being sent to Triple-A Nashville on June 27. With Milwaukee acquiring lefty Kyle Lobstein from the Nationals on Tuesday, Weber is the odd man out on the 40-man roster. The 30-year-old could attract interest on the waiver wire from clubs in search of bullpen depth.