Elliott, whose cap hit will be $2.75 million, will likely split time in Philadelphia's goal with Michal Neuvirth.
Elliott's 2016-17 season ended on a sour note for the Calgary Flames, as he allowed five goals in an overtime loss to the Ducks then was pulled early in Game 4 as Anaheim completed the first-round sweep of Calgary.
As good as Elliott was the last half of the season in getting Calgary to the playoffs, he gave up soft goals in the second, third and fourth games of the series.
"It's just tough to swallow, especially in an elimination game," Elliott said after the Flames bowed out. "It's not how you imagine things happening."
Traded before the 2016 draft after five seasons with the Blues, Elliott was 26-18-3 for the Flames with a 2.55 goals-against average and a .910 save percentage.
The Associated Press contributed to this report.