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.
The Yankees and Mariners have been trading partners several times over the last couple of years, pulling off deals involving Ichiro Suzuki and Jesus Montero.
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.