Brandon Workman attended Bowie High School in Bowie, Texas.  He was a four-year letter winner, playing shortstop and pitcher. As a senior and captain of the team, he had a 10–2 win–loss record with a 0.81 earned run average (ERA) and 171 strikeouts in 76 innings. As a hitter, he batted .481, and earned first-team All-State honors twice, first-team Louisville Slugger High School All-American recognition, and Rawlings All-Region honors. He was drafted by the Philadelphia Phillies in the third round of the 2007 MLB draft, but opted to attend college.

Workman attended the University of Texas at Austin, where he played college baseball for the Texas Longhorns. During his freshman season, he went 5–2 and was named to the honor roll. During his sophomore season, he went 3–5 and held a 4.72 ERA in Big 12 Conference play. He would then have an excellent junior season, before entering the MLB draft. Workman also played for the Wareham Gatemen of the Cape Cod Baseball League, and was a Cape Cod Baseball League All-Star, posting a 3.44 ERA as a freshman.

The Red Sox drafted him in the second round (57th overall pick) of the 2010 MLB draft, and signed him for a signing bonus of $800,000 He spent the 2011 season with the Class A Greenville Drive, appearing in 26 games (all starts) with a 6–7 record and 3.71 ERA.

In 2012, Workman was named the Red Sox's 2012 Minor League Pitcher of the Year, after pitching 20 games (all starts) for the Salem Red Sox and leading the Class A-Advanced Carolina League in fewest baserunners per nine innings, while ranking second in walks plus hits per inning pitched (WHIP) and fourth in ERA. He was promoted to the Portland Sea Dogs of the Class AA Eastern League where he appeared in five games (all starts) and had a 3–1 record and 3.96 ERA.

Workman started the 2013 season with Portland, appearing in 11 games (10 starts) with a 5–1 record and 3.43 ERA. He was promoted to the Pawtucket Red Sox of the Class AAA International League, where he would appear in six games (all starts) with a 3–1 record and 2.80 ERA.

Workman was promoted to the Red Sox in July 2013, after a season-ending foot injury to Andrew Miller. In his major league debut against the Seattle Mariners on July 10th, he pitched two innings in relief, gave up three runs, and struck out four. Through the remainder of the 2013 Red Sox season, he posted a 6–3 record with 4.97 ERA over 20 regular season appearances (3 starts), and did not allow an earned run during seven postseason appearances. He pitched a perfect 8th inning in the decisive Game #6 of the 2013 World Series, setting up closer Koji Uehara. He also recorded his first professional at bat in Game #3 of the World Series, striking out on three consecutive pitches.

Overall, for the 2014 Red Sox, Workman appeared in 19 games (15 starts) and had a 1–10 record with 5.17 ERA. He also appeared in 11 games (all starts) with Triple-A Pawtucket, compiling a 7–1 record with 4.11 ERA.

In April 2015, Workman was placed on the disabled list with elbow soreness. He underwent a platelet-rich plasma (PRP) injection and was ordered not to throw for several weeks. When that was unsuccessful, he underwent Tommy John surgery in June. As a result, he missed the entire season, and during the 2016 season made just ten appearances with Red Sox farm teams, pitching a total of 20 innings and giving up 17 earned runs (7.65 ERA).

In December 2016, Workman signed a one-year contract worth  $635,000 with the Red Sox. He was optioned to Triple-A Pawtucket to start the 2017 season; he would make 18 relief appearances with the PawSox, with a 1.55 ERA and 1.000 WHIP. Workman was called up by the Red Sox on May 2, and made his first MLB appearance since 2014 on May 4th, pitching three scoreless innings. He posted a 3.18 ERA and 1.21 WHIP over ​39 23 innings of relief work.

In January 2018, Workman and the Red Sox avoided arbitration by agreeing to a one-year, $835,000 deal for the 2018 season.  He was optioned to Triple-A Pawtucket prior to the start of the 2018 season, following limited success during spring training (9 appearances, 5.59 ERA, 1.76 WHIP). On June 5th, Workman was called up to the Sox after Drew Pomeranz was placed on the disabled list.  He made 21 relief appearances during June and July, pitching ​18 23 innings with a 2.89 ERA. He was returned to Triple-A on July 26th, when the Red Sox added Nathan Eovaldi to the active roster.

Workman was recalled to Boston from July 31st until August 12th, when Chris Sale was on the disabled list, making five relief appearances and allowing one run in ​5 23 innings (1.59 ERA). He was again called up on August 18th, when Sale went back on the disabled list. For the season, he made 43 relief appearances with the Sox, compiling a 6–1 record with 3.27 ERA and 37 strikeouts in ​41 13 innings. He was on Boston's postseason Roster for the ALDS and ALCS, making three relief appearances and allowing a combined five runs in one inning pitched. He was replaced on the roster by Drew Pomeranz for the World Series.

Workman was included on the Sox Opening Day roster to start the 2019 season. For the season, he appeared in 73 games, compiling a 10–1 record with 16 saves, while striking out 104 batters in ​71 23 innings. He was named Reliever of the Month in the A.L. after saving 7 games with an ERA of 0.00 and 18 strikeouts. He finished the 2019 season as Boston’s closer.

Workman made seven appearances with Boston during the start-delayed 2020 season, registering four saves and a 4.05 ERA. On August 21st, he was traded to the Philadelphia Phillies along with Heath Hembree and cash for Nick Pivetta and Connor Seabold.