Josh Beckett grew up idolizing fellow Texans Nolan Ryan and Roger Clemens. As a youth, he starred on Little League All-Star teams. He later attended Spring High School in Spring, Texas. He had trouble with grades and not paying attention to his coach during his freshman year. His coach was so frustrated with him he threw him off the team. He went through a growth spurt before his sophomore year and added speed to his fastball. He also raised his GPA and was able to get back on the team, where he had a 9–3 record with a 1.18 earned run average (ERA) as a sophomore, tossing three no-hitters.

As a High School junior, Beckett was ranked by Baseball America as the top high school prospect in the country and his team as the top high school baseball team. He went 13–2 and struck out 2.1 batters per inning while walking only 20 batters all season. His high school coach said “I’ve never seen a pitcher with his ability—ever.”

In his senior season, Beckett, by this point nicknamed "Kid Heat," was named the High School player of the year by USA Today. Beckett signed a letter of intent to pitch for Texas A&M University, but he and Josh Hamilton were seen as the top two players available in the 1999 Major League Baseball Draft. Concerned about Beckett's perceived arrogance, the Tampa Bay Devil Rays picked Hamilton with the first pick. Beckett was selected with the second pick by the Florida Marlins. Marlins scouting director Al Avila said at the time, "Beckett has good size and has an overpowering fastball. He's a bulldog on the mound." Showing his confidence, Beckett predicted that he would make it to the Majors within two years and play in an All-Star game by 2001.

Beckett engaged in protracted negotiations with the Marlins, during which he briefly enrolled at Blinn Junior College, but he eventually signed on August 28, 1999 to a four-year $7 million contract that included a $3.625 million signing bonus. In his five seasons with the Marlins, Beckett had a 41–34 record, a 3.46 ERA and struck out a total of 607 batters in 106 games.

In a deal that was made official on Thanksgiving Day 2005, Beckett was traded to the Boston Red Sox along with third baseman Mike Lowell and relief pitcher Guillermo Mota for minor league shortstop Hanley Ramírez and pitchers Aníbal Sánchez, Jesús Delgado and Harvey García. Beckett and Lowell were among a prominent list of veterans the Marlins traded in an effort to shed salary. This was organizationally termed a market correction.  In his first start with the Red Sox, Beckett allowed only one run in seven innings to pick up the win against the Texas Rangers on April 5, 2006.

Beckett was the first Red Sox pitcher to hit a home run in 35 years, since the advent of the designated hitter rule, when he took Phillies' pitcher Brett Myers deep during an interleague game on May 20, 2006.  On July 18, he signed a three-year, $30 million contract extension with a $10 million club option for 2010.  Beckett completed his first season with the Red Sox with a record of 16–11 and a 5.01 ERA. In 204 23 innings, he gave up 191 hits and struck out 158 batters while walking 74. He also allowed 36 home runs, tied for second most in the majors.

At the start of the 2007 season, Beckett adjusted to throwing more breaking pitches and fewer fastballs. At the same time, he learned to locate his pitches rather than simply get strikes by power.  He reduced his walks and home runs allowed by nearly half, contributing to his success in 2007.  Beckett became one of six Red Sox pitchers in history to win their first seven starts. George Winter and Mickey Harris both won their first seven starts in a season, and Babe Ruth, Dave Ferriss and Roger Moret all won their first eight starts in a season.  After a strong first half, posting a 12–2 record with a 3.44 ERA, he was selected to the American League team in the 2007 MLB All-Star Game.  Beckett earned the victory in the game after pitching two innings, giving up only one hit, and striking out two.  Beckett became the first pitcher to win 20 games in a season since 2005, finishing the season with a record of 20–7, a 3.27 ERA, 194 strikeouts, a 1.14 WHIP, and only 40 walks and 17 home runs allowed.

Beckett started the first game of the 2007 American League Championship Series (ALCS) and pitched six innings for the win and in game five he struck out 11 in eight innings. Beckett's 2–0 record and 1.93 ERA against the Cleveland Indians earned him the 2007 ALCS MVP Award.  He then started and won the first game of the 2007 World Series against the Colorado Rockies, pitching seven innings, allowing one run on six hits, and striking out nine batters. Boston would go on to sweep the Rockies in the series.

On May 8, 2008, Beckett recorded his 1,000th career strikeout, when Brandon Inge of the Detroit Tigers struck out swinging in the seventh inning.  He was 12–10 with a 4.03 ERA in 27 starts. In game three of the 2008 American League Division Series against the Anaheim Angels he allowed four runs in five innings  He then made two starts in the 2008 ALCS against the Tampa Bay Rays and was 1–0 but had a high 9.64 ERA.

In 2009, during his first Opening Day start with the Red Sox, Beckett struck out 10 through seven innings allowing only one run and two hits in a 5–3 victory over the Rays.  On April 14, 2009, MLB fined and suspended him six games for intentionally throwing over the head of Angels outfielder Bobby Abreu.  Beckett later appealed the suspension and got it reduced to five games. On June 20, 2009, he recorded his first complete game shutout in three years against the Atlanta Braves in a duel against former Red Sox pitcher Derek Lowe. The shutout was his first in a Red Sox uniform.  On July 5, 2009, he was selected to represent Boston in the 2009 MLB All Star Game.

Beckett recorded his 100th career win on July 12, 2009, pitching a complete game shutout against the Kansas City Royals at Fenway Park. On August 7, 2009, against the New York Yankees, he engaged in a pitching duel with former Marlins teammate A. J. Burnett that turned into a fifteen inning, five hour and thirty-three minute game. He threw seven shutout innings, as Burnett threw seven and two thirds. The Red Sox eventually lost the game in the bottom of the 15th, when Alex Rodriguez hit a walk-off two run home run.  He was 17–6 on the season, with a 3.86 ERA in 32 starts.  He lost his one start in the postseason, to the Angels in game two of the 2009 ALDS.

On April 5, 2010, the Red Sox and Beckett agreed to a four-year, $68 million contract extension, through 2014.  On May 7, he allowed nine runs, struck out eight and also hit two batters. This was the first time a Major League pitcher had that combination of stats in a single game since Jack Coombs of the Philadelphia Athletics during the 1911 season. He was placed on the disabled list on May 19 with a lower back strain and returned from the injury on July 23.  On September 16, he recorded his 1,000th strikeout as a member of the Red Sox against Tampa Bay's Ben Zobrist in the sixth inning.  In 21 starts in 2010, he was 6–6 with a 5.78 ERA.

In 2011 he posted career highs in ERA (2.89), opponent batting average (.211) and WHIP (1.03).  He was 13–7 in 30 games and was selected to his third All-Star Game.  At the end of the 2011 season, the Red Sox stumbled and failed to make the playoffs. Beckett and two more starting pitchers (John Lackey and Jon Lester) were in the center of a controversy where the three drank alcohol during games, where they weren't pitching, and also ate fried chicken and played video games. Beckett was noted as the leader of this and some cited this behavior as part of the reason for the team's poor play down the stretch.

Beckett struggled in the 2012 season, he went 5–11 with a 5.23 ERA as a Red Sox.  He was also the center of yet another controversy when it was reported that he played several rounds of golf despite having been scratched from his start due to a lat muscle injury.  In what would turn out to be his final start with the Red Sox, he allowed four runs in six innings on August 19, 2012 against the Yankees. Over seven seasons, he started 194 regular season games for the Red Sox with a 89–58 record, a 4.17 ERA and 1,108 strikeouts.

On August 25, 2012, he was traded to the Los Angeles Dodgers (along with Adrian Gonzalez, Carl Crawford and Nick Punto and $11 million in cash) for James Loney, Iván DeJesús, Jr., Allen Webster, and two players to be named later (Jerry Sands and Rubby De La Rosa).

On January 22, 2011, he married Holly Fisher, an aeronautics engineer and former high school classmate. Josh and Holly have two daughters, Ryann and Sage.

Beckett is an avid deer hunter and has been since childhood. He was the 2002 winner of the Muy Grande Deer Contest for bringing down the largest buck during the Texas deer hunting season. He owns Herradura Ranch, a 7,000 acres deer-hunting ranch outside of Cotulla, Texas.