Fox Sports Midwest's Andy Strickland reported Elliott will receive a two-year, $2.75 million deal from the Flyers.
Elliott split time with Chad Johnson in goal, starting 45 games and going 26-18-3 with a 2.55 goals-against average, .910 save percentage and two shutouts during the regular season.
The two-time All-Star struggled mightily in the playoffs, however, as he went 0-3 with a 3.89 goals-against average and .880 save percentage in four appearances. Calgary was swept out of the first round of the postseason by the Anaheim Ducks.
Elliott's playoff showing was a far cry from the performances he often put up during his five seasons with the Blues.
With St. Louis, Elliott went 104-46-16 with a sparkling 2.01 goals-against average, .925 save percentage and 25 shutouts.
He also split the 2011-12 William M. Jennings Trophy with Jaroslav Halak, as they combined to allow the fewest goals in the NHL that season.
Despite his solid numbers, Elliott was dealt due to the emergence of young goalie Jake Allen, who is seemingly entrenched as the Blues' long-term goalie.
Elliott may not be a workhorse in the crease, but he has proved capable of being an asset when placed in the right situation.
Aside from the 2009-10 season when he appeared in 55 games for the Ottawa Senators, Elliott has never played in more than 49 games in a single campaign.
That suggests he isn't in line to be a clear No. 1 goalie, but the fact that he has played well in timeshares over the course of his career is a positive since he will be comfortable regardless of his role.
The Flyers needed to address their goalie situation in free agency. Steve Mason is reportedly going to sign with the Winnipeg Jets, per Jeff Hamilton of the Winnipeg Free Press, leaving a huge hole in net for Philadelphia.
Elliott gives the Flyers a stable veteran presence who has the potential to keep the team competitive and return to the playoffs after missing out last season.