The forward, who has 321 points (160 goals, 161 assists) in 652 NHL games, played with Nottingham of the Elite Ice Hockey League in the United Kingdom last season. He signed a one-year contract earlier Tuesday and has been with the Flyers since signing a professional tryout contract July 17.
Stewart last played in the NHL with the Flames in 2017-18.
Philadelphia will try to start the season with points in its first four games for the first time in eight seasons. The Flyers began the 2011-12 season 4-0-1.
The Flames, who were tied for second with 289 goals last season, have scored 15 goals in six games. They have lost two games in a row.