After graduating from Halifax County High School in South Boston, Virginia, Jeffress was selected by the Milwaukee Brewers as the 16th overall pick in the 2006 Major League Baseball draft. He signed a contract with a $1.55 million signing bonus in 2006. In 2008, he started on the Brevard County Manatees' roster on the restricted list. On August 6, the Milwaukee Brewers organization announced that Jeffress was promoted to their Double-A team, the Huntsville Stars. He began the 2009 season with Huntsville, but struggled and was sent back to Brevard County in May 2009. At the beginning of the 2010 campaign, Jeffress was sent down to the Class A affiliate, the Wisconsin Timber Rattlers. On July 1, 2010, Jeffress was called up to Class A-Advanced Brevard County, where he continued to throw out of the bullpen. He was later promoted to Huntsville. Jeffress was called up to the majors for the first time on September 1, 2010. He made his major league debut that evening, pitching one scoreless inning.
On November 8, 2012, the Toronto Blue Jays received Jeffress from the Royals in exchange for cash considerations. Jeffress was designated for assignment by the Blue Jays on April 6, 2013 after pitching in one game. Jeffress cleared waivers, and was assigned outright to the Triple-A Buffalo Bisons on April 16. Jeffress was sent to the Class A Dunedin Blue Jays on April 25 without having pitched for the Bisons. He was brought up to the Bisons on May 3. His contract was selected by the Blue Jays on September 3 after the Bisons season ended, and the major league rosters expanded. Jeffress was designated for assignment after the game on April 4, 2014. On April 15, after clearing waivers, Jeffress was assigned to Buffalo; however, he chose free agency rather than report to Buffalo.
Return to the Milwaukee Brewers
Jeffress signed a minor league contract with the Milwaukee Brewers on April 18, 2014. He was assigned to the Triple-A Nashville Sounds. The Brewers selected the contract of Jeffress from Nashville on July 21, 2014. Jeffress thrived in his return to Milwaukee, emerging as a stellar setup-man to closer Francisco Rodriguez and posting a 1-1 record with a 1.88 ERA in 29 games. In 2015, after struggles from setup manJonathan Broxton, Jeffress took over as the eight-inning man for Milwaukee. In 2016, Jeffress was slated to be Milwaukee's setup man to closer Will Smith but before spring training could begin, Jeffress was named closer when Smith suffered a knee injury.
Texas Rangers
On August 1, 2016, the Brewers traded Jeffress and Jonathan Lucroy to the Texas Rangers for Lewis Brinson, Luis Ortiz, and a player to be named later. After a 2016 season on-par with his career statistics, Jeffress struggled with the Rangers in 2017. He posted a 5.31 ERA and a 1-2 record over 40.2 innings while with the Rangers that season.
Third stint with Milwaukee
On July 31, 2017, the Rangers traded Jeffress to the Milwaukee Brewers for Tayler Scott. As of June 12, 2018, Jeffress' ERA, WHIP, and K/BB ratio were career bests. On July 12, 2018 Jeffress was named to his first All-Star team as a replacement for Sean Doolittle. He was released by the Brewers on September 1, 2019.
Chicago Cubs
On January 28, 2020, Jeffress was signed by the Chicago Cubs for a 1 year, $850,000 major league contract, with possibility of Jeffress earning an additional $200,000 based on games pitched.
Personal life
On August 30, 2007, Jeffress was suspended for 50 games after testing positive for "a drug of abuse," which was reportedly marijuana. This was not his first positive test; he was given a warning for his first offense. In June 2009, he tested positive a third time and was suspended for 100 games. One more positive test will result in a lifetime ban for Jeffress. In late June 2013 while with the Triple-A Buffalo Bisons, Jeffress was diagnosed with juvenile epilepsy, which gave an explanation to the high anxiety and seizures that he had experienced through most of his adult life. Before receiving a proper diagnosis, he self-medicated with marijuana. On August 26, 2016, Jeffress was arrested for driving while intoxicated.