The Rangers will receive minor league outfielders Antonio Cabello and Josh Stowers, with the Yankees also getting cash considerations in the deal.
Texas is expected to absorb almost the entirety of the $27 million owed to Odor, sources told ESPN's Jeff Passan. He's due $12 million this year, $12 million in 2022 and a $3 million buyout on a $13 million club option in 2023.
Odor spent the past seven seasons as the Rangers' starting second baseman, but an attempt to convert him into a third baseman ended with Odor failing to make the team's Opening Day roster.
Odor, 27, led Texas with 30 RBIs in 38 games during the pandemic-shortened 2020 season and matched Joey Gallo with a team-best 10 homers. But Odor hit only .167, with seven of his 11 hits in September being homers, and struck out 47 times in 138 at-bats. He hit .205 in a full 2019 season. In 858 games for the Rangers since his debut in 2014, he has hit .237 with 146 homers and 458 RBIs.
Information from The Associated Press was used in this report.