Terms of the deal weren't revealed, but the Philadelphia Inquirer reported it was for three years for a total of $12.3 million.
The 25-year-old was set to become a restricted free agent at the end of the current season.
The signing could serve to resolve the Flyers' revolving door at the goalie position. The team bought out the final seven years of a 2011 deal signed by Ilya Bryzgalov and in 2012 traded Sergei Bobrovsky to Columbus, where he went on to win the Vezina Trophy as the league's top goaltender.
Mason has racked up a 19-11-5 record with a 2.48 goals-against average and a .917 save percentage this season -- his first full campaign with the Flyers.
He sports a 119-112-32 career record with 20 shutouts, a 2.82 GAA and a .906 save percentage for the Blue Jackets and Flyers.