In return, the Mariners reportedly will receive right fielder Jay Bruce and several prospects -- right-hander Justin Dunn, a first-rounder in 2016; outfielder Jarred Kelenic, the sixth overall pick in 2018; right-handed reliever Anthony Swarzak and right-hander pitcher Gerson Bautista.
The Mariners also are sending $20 million to New York.
The trade is contingent upon players passing their physical exams. The deal could be announced as soon as Monday
Cano, who waived his no-trade clause as part of the deal, has five years, $120 million remaining on the 10-year, $240M contract he signed with Seattle in December 2013 -- after he starred for the Yankees from 2005 to 2013.
Diaz, 24, is the prize in the deal. He had a 1.96 ERA and led the majors with 57 saves last season.
Cano, 36, was suspended for 80 games last season for PEDs. He hit .303 with 10 home runs and 50 RBIs in 80 games.