The teams announced the trade Wednesday night.
The 28-year-old Kelley went 2-4 with a 3.25 ERA in 47 appearances for Seattle last season and figures to fill a middle-relief role with the Yankees. He was designated for assignment by the Mariners on Feb. 7 when the club signed catcher Kelly Shoppach.
About a week earlier, Kelley and the Mariners agreed to a $935,000, one-year contract that avoided salary arbitration. Kelley is 10-9 with a 3.52 ERA in four big league seasons, all with Seattle.
Almonte, 23, batted .276 with four homers, 25 RBIs and 30 steals in 78 games for Double-A Trenton last season.