Canning signed a one-year, $4.25 million contract with the Mets on Wednesday, Ken Rosenthal of The Athletic reports.
The Angels traded Canning to Atlanta on Thursday in exchange for Jorge Soler.
Canning did not factor into the decision in a loss to the Rangers on Saturday, allowing two runs on four hits and two walks over five innings while striking out four.
Canning (6-13) got the win Tuesday against the White Sox after throwing six scoreless innings while allowing just three hits and two walks and striking out six.
Canning (4-12) took the loss Wednesday, giving up three runs on five hits and four walks over five innings as the Angels fell 3-2 to the Tigers. He struck out four.
Canning is scheduled to start Wednesday's game against the Tigers at Comerica Park.
Canning is in line to serve as a bulk reliever in Thursday's contest against the Blue Jays, Jeff Fletcher of The Orange County Register reports.
Canning (4-11) took the loss against Atlanta on Saturday, allowing seven runs on eight hits and one walk over 4.1 innings while striking out three.
Canning came away with a no-decision in Saturday's 5-4 extra-inning loss to the Nationals, giving up four runs on eight hits over seven innings. He didn't walk or strike out a batter.
Canning (elbow) is expected to draw the start Wednesday on the road against the Mariners, Jeff Fletcher of The Orange County Register reports.