St. Louis will receive MLB reliever Dominic Leone and minor-league right-hander Conner Greene in exchange for Grichuk.
The Cardinals, meanwhile, will add an established middle-relief option to their bullpen in Leone, who posted an impressive 2.56 ERA and 1.05 WHIP in 70.1 innings of work last season for the Jays.
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Leone, a 2009 NFA graduate, played at Clemson for three years and was drafted by the Mariners in the 16th round in 2012. The 26-year-old has hit 20-plus home runs in back-to-back seasons, even though he was sent to Triple-A for stretches of both campaigns. Greene, 22, spent the 2017 season with the Blue Jays' Class AA New Hampshire Fisher Cats, posting a 5.29 ERA with 92 strikeouts and a WHIP of 1.69 in 132 2/3 innings.
The Cardinals previously made a splash back in December when St. Louis acquired another outfielder in Marcell Ozuna from the Miami Marlins. With Ozuna and Pham locked into starting spots, and former center fielder Dexter Fowler expected to move to right, Grichuk was the odd man out of the projected lineup. "We knew there would be a possibility", Grichuk said over the weekend of the possibility of a trade.