He made his MLB debut for the White Sox in 2009 and has also played for the Arizona Diamondbacks, Pittsburgh Pirates, Los Angeles Dodgers, Toronto Blue Jays, Washington Nationals and San Diego Padres.

Hudson was on the mound at the end of Game 7 of the 2019 World Series to clinch the Nationals' first championship in franchise history.

For the remainder of the 2008 season he was assigned to the White Sox rookie-level affiliate, the Great Falls Voyagers, where he posted a win–loss record of 5–4 and an ERA of 3.36 in 14 starts.

Hudson's rapid rise through the White Sox minor league system continued in Birmingham, where he posted a record of 7–0, with a 1.60 ERA.

The White Sox promoted Hudson to the majors for the first time on September 3, 2009, after posting a 14–5 record and a 2.32 ERA, and striking out 166 in 147+1⁄3 innings at four minor league levels.

He received his first win in his second start on September 27, 2009, allowing two earned runs over six innings at U.S. Cellular Field against the Detroit Tigers.

[6] On July 30, 2010, the White Sox traded Hudson and minor league pitcher David Holmberg to the Arizona Diamondbacks for Edwin Jackson.

He helped lead the team to an NL West division title but faltered in the NLDS as he gave up five runs in Game 2 and was credited with the loss.

In a rehab start with the Double-A Mobile BayBears on June 4, 2013, Hudson re-tore his ulnar collateral ligament.

Hudson underwent Tommy John surgery for the second time in his career on June 18, 2013, which shut him down for the entire 2013 season.

[11] On February 22, 2018, the Pirates traded Hudson, Tristan Gray, and cash considerations to the Tampa Bay Rays for Corey Dickerson.

[14] He made the Dodgers major league roster and pitched in 40 games for them (with one start) and was 3–2 with a 4.11 ERA in 46 innings, before missing the last month of the season with an arm injury.

[9] Hudson missed Game 1 of the 2019 National League Championship Series to be with his wife in Scottsdale, Arizona, to witness the birth of their third daughter.

[23] On July 30, 2021, Hudson was traded to the San Diego Padres in exchange for Mason Thompson and Jordy Barley.

The Braves–Padres game on that same day had been suspended, and by the time it resumed on September 24, 2021, Hudson had joined the Padres, and Duvall was a Brave.

[30] He rejoined the Dodgers on June 30[31] and pitched three scoreless innings over three games before straining his MCL in his right knee on July 5, putting him back on the injured list.