Toronto and New York announced the pact on Wednesday. The Blue Jays sent right-handed pitchers Sean Reid-Foley, Yennsy Diaz and Josh Winckowski to the Mets in exchange for the six-year veteran.
Matz, 29, went 0-5 with a 9.68 ERA in nine games as he dealt with shoulder issues last season. He has a career ERA of 4.35.
Matz is expected to slide in behind ace Hyun Jin Ryu and Nate Pearson in Toronto's starting rotation. The Blue Jays staff also could feature a combination of Robbie Ray, Ross Stripling, Julian Merryweather, Thomas Hatch, Trent Thornton and Anthony Kay.
Toronto could still make additional rotational improvements to supplement its other lineup upgrades from the off-season. The Blue Jays also acquired outfielder George Springer and infielder Marcus Semien this winter. Toronto signed relief pitchers Kirby Yates and Tyler Chatwood last week.
Reid-Foley and Diaz were on the Blue Jays' 40-man roster before the trade. Reid-Foley, 25, went 1-0 with a 1.35 ERA in five appearances last season. He went 2-4 with a 4.26 ERA in 2019.
Diaz, 24, was the Blue Jays' No. 26 prospect, according to MLB Pipeline. He allowed two runs and walked four in 2/3 of an inning in his lone MLB appearance in 2019.
Winckowski, 22, was Toronto's No. 27 prospect. He had a 2.69 ERA at the Class A and Class A Advanced level in 2019.