A right-hander who turns 25 on Dec. 10, Cortes was 5-1 with a 5.67 ERA in 32 relief appearances and one start this year after making four relief appearances in his first big league season with the Yankees in 2018.
He was designated for assignment last week to open a roster spot for prospects protected ahead of the winter meeting draft next month.
New York's 2019-20 pool total increased to $5,835,800 with Monday's trade. The Yankees have used $5,762,000 of that, including $5.1 million on Dominican outfielder Jasson Dominguez, $377,500 on Dominican third Enger Castellano and $187,500 on Venezuelan catcher Manuel Palencia.
Seattle has now spent its entire $5.37 million pool and is limited to signing bonuses of $10,000 or less for the current signing year, which ends June 15.