The Yankees sent minor league outfielders Antonio Cabello and Josh Stowers to the Rangers in exchange for Odor and cash considerations, according to the team.
The 27-year-old Odor failed to make the Rangers' Opening Day roster and was designated for assignment April 1. He will provide the Yankees' mostly right-handed lineup with a left-handed bat.
"Hopefully we can help him get that talent out that we've seen flash over the years," Yankees manager Aaron Boone said.
Odor primarily is a second baseman, but he also played third in spring training.
The Yankees optioned right-hander Michael King to their alternate training site to create a space on the active roster. New York then designated infielder Thairo Estrada for assignment to make room for Odor on the 40-man roster.
Odor has a .237 career batting average with 146 home runs and 458 RBIs over seven MLB seasons with the Rangers. He recorded a .167 average with 10 homers and 30 RBIs during the pandemic-shortened 2020 season.
In the spring, Odor batted .200 with two home runs and five RBIs in 35 at-bats for Texas.