Allard, 25, was Atlanta's top choice, No. 14 overall, in the 2015 draft. He was 1-2 with a 7.29 ERA in 10 relief appearances last season while also spending time at Triple-A Round Rock.
Odorizzi, 32, was an All-Star with Minnesota in 2019, when he had a career-best 15 wins.
Allard, drafted from San Clemente (California) High School, made his major league debut with Atlanta in 2018 but appeared in only three games with the Braves before he was traded to Texas in 2019 for righty Chris Martin.
Allard is 9-23 with a 6.07 ERA in 65 career games, including 35 starts. He was used as a starter in 20 games with Round Rock last season.
The Braves acquired Odorizzi from the Houston Astros on Aug. 2 for left-hander Will Smith. Odorizzi, 32, was 6-6 with a 4.40 ERA in a combined 22 games with Houston and Atlanta last season.
Odorizzi has a $6.5 million player option for 2023 and minimum buyout of $3.25 million.
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The Associated Press