The Brewers outrighted White to Triple-A Nashville on Monday after he cleared waivers, Todd Rosiak of the Milwaukee Journal Sentinel reports.
The Brewers designated White for assignment Thursday.
White was acquired by Milwaukee on Friday in exchange for cash considerations.
The Giants designated White for assignment on Sunday, Shayna Rubin of the San Francisco Chronicle reports.
White was designated for assignment by the Blue Jays on Tuesday, Hazel Mae of Sportsnet reports.
White (1-0) picked up the win Sunday against the Rays, allowing just one walk over three scoreless, hitless relief innings without striking out a batter.
White allowed two runs on five hits and a walk over three innings in Monday's Grapefruit League game against the Rays. He struck out two.
White is one of the top candidates to step into the rotation if either or both of Kevin Gausman (shoulder) and Alek Manoah (shoulder) aren't ready for Opening Day, Kaitlyn McGrath of The Athletic reports.
White sat 94-95 mph with his fastball during his first bullpen session this spring, Kaitlyn McGrath of The Athletic reports.
White is projected to break camp on the Blue Jays' 26-man roster by Gregor Chisholm of The Toronto Star.