The Yankees announced the roster moves Wednesday. Ellsbury had more than $26 million left in his seven-year, $153 million contract that he signed with the club in December 2013.
The club will owe Ellsbury over $21 million for next season, along with a $5 million buyout of a $21 million team option for 2021.
Ellsbury, who hasn't played with the Yankees since 2017 due to multiple injuries, was cut to clear a spot on the team's 40-man roster as New York added seven players to protect them from next month's Rule 5 draft.
Ellsbury, a two-time World Series champion and 2011 All-Star choice, had a .264 batting average with 39 home runs, 198 RBIs and 102 stolen bases in 520 games across four seasons with the Yankees. The 36-year-old outfielder spent his first seven MLB seasons with the Boston Red Sox.
The Yankees designated Bird, 27, and left-hander Nestor Cortes Jr. for assignment. Bird joined the club in 2015 and finished the season with 11 home runs and 31 RBIs in 46 games.
Bird then missed the entire 2016 campaign after undergoing surgery to repair a torn labrum in his right shoulder. Multiple injuries forced him to sit out large portions of the next three seasons.
The Yankees added outfielder Estevan Florial to the major league roster, along with right-handed pitchers Deivi Garcia, Luis Gil, Brooks Kriske, Luis Medina, Nick Nelson and Miguel Yajure.