The team confirmed the news on its website, and Granqvist later confirmed it via his Twitter account.
"I am very excited & inspired to work with & support Ilya Bryzgalov next week here in Karlstad," Granqvist wrote.
Granqvist spoke with Bryzgalov via Skype before the club agreed to allow him to train with them.
Bryzgalov is hoping to return to the NHL next season, though he's unlikely to obtain a starter's role; he'll have to accept a backup position and climb his way back into No. 1 goalie status.
The native of Togliatti, Russia, posted a 19-17-3 record with the Flyers this past season, along with a 2.79 goals-against-average and a .900 save percentage.
The Flyers are responsible for paying Bryzgalov $23 million over the next 14 seasons -- roughly $1.642 million per year.
In 425 career NHL regular-season games with the Anaheim Ducks, Phoenix Coyotes and Flyers, Bryzgalov has accumulated a 208-149-45 record with a 2.55 goals-against-average, a .913 save percentage and 30 shutouts.
He was originally drafted by the Ducks in the second-round (44th overall) of the 2000 NHL Entry Draft.