The Mets are getting right-handed pitchers Sean Reid-Foley, Yennsy Diáz and Josh Winckowski in the trade.
Matz, a 29-year-old left-hander, agreed to a $5.2 million, one-year deal with the Mets in December.
That deal came after he had the poorest of his six seasons, going 0-5 with a 9.68 ERA while earning $1,851,852 in prorated pay from a $5 million salary. He was dropped from the rotation after starting 0-4 with a 9.00 ERA in five starts, then made three relief appearances along with a spot start.
Matz is 31-41 with a 4.35 ERA over 107 career starts and five relief appearances.
The Jays have had a busy offseason, highlighted by the addition of outfielder George Springer on a $150 million, six-year deal.
Earlier this week, infielder Marcus Semien reached agreement on a one-year, $18 million contract, a source familiar with the deal told Passan.