New York will pay Odor the league minimum of $570,500 while the Rangers pay the balance of his salary, according to Jon Heyman of MLB Network.
The Yankees designated infielder Thairo Estrada for assignment to make room on the roster for Odor and also optioned right-hander Michael King to their alternate training site.
Odor is due $12 million in 2021, $12 million in 2022, and has a $13-million club option in 2023 with a $3-million buyout.
Texas designated him for assignment last week. He signed a six-year, $49.5-million extension prior to the 2017 campaign.
Odor has spent his entire seven-year career with the Rangers, making 814 starts at second base. The 27-year-old owns a .237/.289/.439 slash line with 146 home runs and 458 RBIs. He's hit 30-plus homers in a single season three different times.
Yankees manager Aaron Boone said Odor could play third base when he joins the team, according to Brendan Kuty of NJ.com.
Meanwhile, Stowers, 24, has yet to play above Single-A during his pro career, while Cabello, 20, was in rookie ball in 2019.