The Athletics agreed to a three-year, $67 million contract with Severino on Thursday, Jeff Passan of ESPN.com reports.
Severino has rejected the Mets' one-year, $21.05 million qualifying offer, Tim Healey of Newsday reports.
The Mets extended a one-year, $21.05 million qualifying offer to Severino on Monday, Jon Heyman of the New York Post reports.
Severino will start Wednesday in Game 3 of the NLCS against the Dodgers, Anthony DiComo of MLB.com reports.
Severino will start Sunday in Game 2 of the NLDS against the Phillies, Mike Puma of the New York Post reports.
Severino will start Game 1 of the wild-card series against the Brewers on Tuesday, Anthony DiComo of MLB.com reports.
Severino's next start will come during the wild-card series after the Mets called up Joey Lucchesi to start the second game of Monday's doubleheader in Atlanta, Mike Puma of the New York Post reports.
Severino will start Game 2 of Monday's doubleheader versus Atlanta, if necessary, Anthony DiComo of MLB.com reports.
Severino (11-7) took the loss Tuesday, giving up four runs on seven hits and a walk over four innings as the Mets fell 5-1 to Atlanta. He struck out five.
Severino did not factor into the decision Sunday, allowing one run on five hits and two walks over 6.2 innings against the Reds. He struck out eight.