Odorizzi attended Highland High School in Highland, Illinois, where he helped lead the Highland Bulldogs to the Illinois state championship.
The Milwaukee Brewers selected Odorizzi in the first round, with the 32nd overall choice, of the 2008 Major League Baseball draft. He had a 9–9 record, a 3.68 earned run average (ERA), and 197 strikeouts in the Milwaukee Brewers system. He played for the Arizona Brewers (2008), Helena Brewers (2009) and the Wisconsin Timber Rattlers (2010).
On December 17, 2010, the Brewers traded Odorizzi, Alcides Escobar, Jeremy Jeffress, and Lorenzo Cain to the Royals for Zack Greinke and Yuniesky Betancourt. Baseball America ranked Odorizzi as the 69th best prospect in baseball prior to the 2011 season and the 23rd best prospect at midseason. After the 2011 season, he was named the fifth best prospect in the Double-A Texas League. He was named to appear in the 2012 All-Star Futures Game. Odorizzi split time in 2012 between the Royals Double-A affiliate Northwest Arkansas Naturals and Triple-A Omaha Storm Chasers, posting an overall record of 15-5 and a 3.03 ERA. On September 16, 2012, the Royals purchased Odorizzi's contract from Class AAA Omaha. He made two starts for the team before season's end.
On December 9, 2012, the Royals traded Odorizzi to the Tampa Bay Rays (along with Mike Montgomery, Patrick Leonard, and Wil Myers) in exchange for James Shields and Wade Davis. He was optioned to the Triple-A Durham Bulls on March 12. In early May, he threw a combined no-hitter for the Bulls against the Pawtucket Red Sox. He was recalled by the Rays on May 20 to start in Toronto against the Blue Jays. He was sent back to the Bulls on May 29. He was recalled on August 29 for a start against the Los Angeles Angels of Anaheim, and optioned back to Durham the next day. He was recalled on September 20.
Odorizzi spent majority of the 2013 season in the minor leagues posting a 9-6 with a 3.33 ERA in 22 Starts with the Durham Bulls. He got a late call up at the end of 2013, playing in 7 games (4 starts) and had a 3.94 ERA.
At 23 years old, Odorizzi was the fourth pitcher in the rotation for the majority of the season. He plated moderately well, posting an 11-13 won-lost record, and a 4.13 ERA in 33 starts, pitching 168 innings with 174 strikeouts. He came in 8th for AL Rookie of the Year.
In the 2015 season, Odorizzi had an impressive performance. He posted a record of 9-9 with an ERA of 3.25 and FIP of 3.16 in 169.1 innings, despite only making 28 starts.
In the 2016 season, Odorizzi went 10-6 with an ERA of 3.69 in 33 games over 187.2 innings.
Odorizzi's flyball tendencies led to his struggles in the power surge of baseball that occurred in recent years. Odorizzi's inability to keep the ball on the ground saw him giving up an incredibly large number of home runs, in fact (as of July 26), 18.3% of all fly balls hit against Odorizzi went for a home run, up 7.2% from his career average (11.1%). As of July 26, his ERA had ballooned to 4.47, an FIP of 5.74, and had allowed 23 home runs in 18 games, even with these stats, Odorizzi had a winning record of 6-4. On July 26, the Rays put Odorizzi on the ten-day DL with lower back strain. On August 9, Odorizzi was activated from the DL.
Odorizzi throws five pitches. He leads with a four-seam fastball at 91–93 mph. He also has a cutter (mid 80s), slider (low 80s), splitter (baseball) (mid 80s), and curveball (low-mid 70s). The slider is mostly used against right-handed hitters, the changeup mostly against lefties.
Scouts originally regarded his fastball as his best pitch and his changeup as the least developed. With the help of Alex Cobb, Odorizzi developed "the thing": a split-change similar to Cobb's main strikeout pitch. This led to Odorizzi winning the 5th starter's job in spring training in 2014.