He has played in Major League Baseball (MLB) for the Tampa Bay Rays, San Francisco Giants, Texas Rangers, Detroit Tigers, Philadelphia Phillies, Los Angeles Angels, Cleveland Guardians, and Miami Marlins and in Nippon Professional Baseball (NPB) for the Fukuoka SoftBank Hawks.

Although he had committed to play college baseball with the University of New Mexico, Moore chose to sign a professional contract with the Rays after they selected him in the 2007 MLB draft.

In 2019, the Tigers signed Moore to a one-year contract, hoping for a rebound season, but he played only two games before suffering a season-ending knee injury.

[4] Moore experienced a growth spurt between his sophomore and junior year of high school, which caught the attention of college recruiters and professional scouts.

[7] On June 8, 2009, Moore was named the South Atlantic League Pitcher of the Week after throwing seven shutout innings in a 10–2 win over the Asheville Tourists.

[9] Mitch Lukevics, the Rays' director of minor-league operations, told FoxSports.com that, in both 2009 and 2010, Moore was "off to a bad start, and the technique [was] not where it need[ed] to be", but he found his stride over the course of the season.

[7] Moore was called up to the Rays on September 11, 2011,[11] and made his MLB debut three days later, giving up a two-run home run to Matt Wieters in the eighth inning of a 6–2 loss against the Baltimore Orioles.

[12] His performance recovered in time for his first major league start on September 22, becoming the first pitcher in MLB history to pitch 11 strikeouts in five innings or fewer against the New York Yankees.

[13] Moore was given the start in Game 1 of the 2011 American League Division Series (ALDS) against the Texas Rangers, pitching seven shutout innings in a 9–0 victory for the Rays.

[16] Moore began with the Rays in 2012 as part of a five-player starting rotation that also included James Shields, David Price, Jeremy Hellickson, and Jeff Niemann.

[17] On June 15, Moore combined with relievers Burke Badenhop and Brandon Gomes to pitch a one-hit shutout against the Miami Marlins, winning 11–0 and breaking a three-game losing streak.

[15] Returning to the Rays in 2013, Moore became the first left-handed American League (AL) pitcher to begin a season with an 8–0 record at age 23 or younger since Babe Ruth in 1917.

He exited the mound in the middle of an April 7 game against the Kansas City Royals, and realized after an afternoon throwing session that he could no longer pitch.

Moore underwent Tommy John surgery on April 22, 2014, to replace a partially torn ulnar collateral ligament, and was sidelined for the remainder of the season.

[34] On August 1, 2016, the Rays traded Moore to the San Francisco Giants in exchange for third baseman Matt Duffy and prospects Lucius Fox and Michael Santos.

Dodgers shortstop Corey Seager hit a single in the bottom of the ninth inning, and reliever Santiago Casilla came in to pitch the final out of the Giants' 4–0 win.

Giants manager Bruce Bochy pulled Moore before the final inning, and the Chicago Cubs overcame a 5–2 deficit to win the game and the series.

[41] On December 15, 2017, the Giants traded Moore to the Texas Rangers in exchange for pitching prospects Sam Wolff and Israel Cruz.

[45] On December 4, 2018, the Detroit Tigers signed Moore to a one-year, $2.5 million contract in anticipation that he would follow Mike Fiers as a low-risk pitcher heading into a rebound season.

[47] He underwent meniscus surgery on April 14, and three days later, Tigers manager Ron Gardenhire announced that Moore would miss the rest of the MLB season.

[49] On December 26, 2019, Moore signed a one-year, US$3.5 million (¥384,000,000) contract with the Fukuoka SoftBank Hawks of Nippon Professional Baseball (NPB), who were looking to rebuild their pitching rotation after losing Ariel Miranda and Robert Suárez.

[52] Moore pitched seven shutout innings, including five strikeouts, in Game 3 of the 2020 Japan Series, and the Hawks came within one out of a combined no-hitter in their 4–0 victory over the Yomiuri Giants.

[54] Because professional baseball returned to play in Japan earlier than in the US, Moore was able to pitch 85 innings in 2020, one more than MLB season leader Lance Lynn.

[56] His poor performance, coupled with time spent on the COVID-19 protocol list, led to his removal from the starting rotation and replacement with veteran Phillies pitcher Vince Velasquez.

[57] Back spasms caused Moore to miss over a month of pitching, from May 20 to June 25, at which point he was reactivated to start the second game of a doubleheader against the Mets.

[76] After returning from Tommy John surgery, however, Moore struggled with his pitch velocity and control, giving up large numbers of earned runs as he threw balls at hittable speeds and strike zone locations.

[77] His time in the NPB showed an improved performance, and Phillies manager Joe Girardi was keen to sign Moore in the hopes that he would add depth to the back end of the Phillies' starting rotation, serving as a player who has "pitched in tough situations" and could contend with aces Aaron Nola and Zack Wheeler.

[79] He and reliever Dellin Betances are known for having a unique grip on their four-seam fastball, in which they tuck their thumb under the ball, which some sports journalists and fellow pitchers believe negatively impacts their pitch control.