"He's the best goalie we've ever had," Dorion told reporters, according to TSN. "It's time for us to take another direction, and we thank him for everything he did."
Anderson, 39, a three-time All-Star, is the Senators' all-time leader in games played by a goaltender (435), wins (202), losses (168) and saves (12,447). He was 11-17-2 in 34 games last season.
Anderson led the Senators to within one game of the Stanley Cup Final in 2016-17, losing in double overtime of Game 7 to Pittsburgh in the conference finals. He did it after taking time off during the season to be with his wife, who was treated for and recovered from throat cancer.
Anderson was traded to Ottawa in 2011 by the Colorado Avalanche.