To clear room on the 40-man roster for Jeffress, the Brewers transferred right-hander Jim Henderson to the 60-day disabled list.
A former top prospect in the organization, Jeffress is 4-1 with a 1.51 ERA in 30 appearances for Nashville.
The Brewers signed Jeffress to a minor-league deal in April, bringing Milwaukee's 2006 first-round pick back into the organization.
Jeffress was designated for assignment by Toronto in April after beginning the season on the team's Opening Day roster. The 26-year-old allowed four earned runs in 3 1/3 innings for the Blue Jays this season before being let go.
Traded by the Brewers to the Royals as part of the Zack Greinke trade, Jeffress walked 18 and struck out 45 in 41 1/3 innings for the Sounds this season.
Jeffress has had his share of troubles off the field, including a 50-game and a 100-game suspension for marijuana use. One more positive test would mean Jeffress is banned from baseball for life. He's also battled juvenile epilepsy leading to seizures and anxiety.
The talent has always been there, however, as the Brewers gave Jeffress a $1.55 million signing bonus after selecting him 16th overall out of Halifax County High School (Va.) in 2006.
Jeffress made his major-league debut with the Brewers in 2010, posting a 2.70 ERA in 10 innings out of the bullpen. He pitched in 14 games with the Royals in 2011 and 13 games in 2012 before being traded to Toronto.