Beltran, 39, is batting .304 with 22 home runs and 64 RBIs this season for the Yankees. He is in the final year of a three-year, $45 million contract and will be a free agent after this season.
Tate, 22, was the Rangers' first-round pick in the 2015 draft. The right-hander is 3-3 with a 5.12 ERA in 17 games (16 starts) with the Hickory Crawdads, the Rangers' Class A team in the South Atlantic League.
In addition to Tate, the Yankees will also receive minor league right-handed pitchers Erik Swanson and Nick Green from the Rangers.
The trade was first reported by Yahoo! Sports.