Almonte, 23, hit .276 for Double-A Trenton last season and had 30 stolen bases in 78 games. He has spent the past seven years in the Yankees' system since signing as a 17-year-old out of the Dominican Republic.
The 5-foot-9, 205-pounder hit four home runs with 25 RBIs and posted a .350 on-base percentage last year in his first season in Double-A ball while playing all three outfield positions.
Almonte has stolen 176 bases in 573 Minor League games, including 29 or more in four different seasons.
Kelley, 28, pitched parts of the past four seasons for Seattle with a 10-9 record and 3.52 ERA in 120 appearances. He was 2-4 with a 3.25 ERA last year while throwing 44 1/3 innings in 47 outings, but the Mariners designated him in order to make room on the 40-man roster for catcher Kelly Shoppach.
Kelley is earning $935,000 this season after agreeing to a one-year deal in his second season of arbitration eligibility.
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.