Stevens took over for fired head coach Ken Hitchcock on Oct. 22.
"I'm excited," Stevens said in a statement. "I know that we have work to do here, but I do see a lot of potential for this hockey team. I want to be the guy who brings success here. I've been in Philadelphia for a long time and I know what it means to win here. I've won championships at the minor-league level and I'd love to have the chance to do it at the NHL level."
The Flyers had a 4-7-1 record under Stevens heading into Monday night's game with Pittsburgh. The 40-year-old native of Campbellton, N.B., joined Hitchcock's staff as an assistant last June after being head coach of the AHL's Philadelphia Phantoms for six seasons. He led the team to the Calder Cup AHL championship in 2004-05.