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. He was an Eastern League midseason All-Star.
To make room for Kelley on the 40-man roster, the Yankees placed third baseman Alex Rodriguez on the 60-day disabled list. Rodriguez is recovering from hip surgery and is not expected back until at least the All-Star break.
New York's 40-man roster is now full.