Per Ken Rosenthal of The Athletic, the Yankees will receive outfielder Jabari Blash in return.
Rosenthal added that the Padres are reportedly absorbing all of Headley's $13 million salary for 2018, which will aid the Yankees in achieving owner Hal Steinbrenner's stated goal of getting under the $197 million luxury tax threshold.
The 33-year-old Headley spent the first seven seasons of his career with the Padres before a 2014 trade to the Yankees.
Last season, Headley played both third base and first base for the Yanks, and he finished the campaign with a .273 batting average, 12 home runs and 61 RBI, which represented his best overall production since 2012.
That season, Headley hit .286 with a career-high 31 homers and 115 RBI for the Padres.
The 26-year-old Mitchell has spent time as both a starter and a reliever with the Yankees over the past four seasons.
In 2017, he went 1-1 with a 5.79 ERA in 20 appearances, including one start. For his career, Mitchell has a 4.94 ERA in 48 games.
Blash is a 28-year-old outfielder with 99 games of MLB experience to his credit. Last season, he hit .213 with five home runs and 16 RBI in San Diego.
He may be hard-pressed to make New York's major league roster since it currently boasts the likes of Aaron Judge, Giancarlo Stanton, Brett Gardner, Jacoby Ellsbury, Aaron Hicks and Clint Frazier in the outfield.
The trade was primarily a salary dump for the Yankees, and it opens up another potential spot for top prospect Gleyber Torres to enter the starting lineup in 2018.