The Mets declined Maton's $7.75 million club option for 2025 on Monday, Jon Heyman of the New York Post reports.
Maton (2-2) picked up the win Thursday in a 3-2 extra-inning victory over Atlanta, throwing a scoreless 10th inning without a walk or a strikeout.
The Rays traded Maton to the Mets on Tuesday in exchange for a player to be named later or cash.
Maton picked up the save over the Mets on Saturday, pitching a scoreless ninth inning while issuing one walk.
Maton signed a contract with the Rays on Saturday, Mark Feinsand of MLB.com reports.
The Astros reinstated Maton (elbow) from the 15-day injured list Monday.
Maton (elbow) is beginning a rehab assignment Friday with Triple-A Sugar Land, Matt Kawahara of the Houston Chronicle reports.
Maton (elbow) threw a bullpen session at Minute Maid Park on Wednesday and could begin a rehab assignment at Triple-A Sugar Land on Friday, Matt Kawahara of the Houston Chronicle reports.
Maton (elbow) could return from the 15-day injured list Sunday when first eligible, Brian McTaggart of MLB.com reports.
Maton (elbow) threw off a mound Saturday, Chandler Rome of The Athletic reports.