The deal is believed to be worth a base salary of $1 million, with $1 million available in bonuses.
Jagr, who will turn 46 in February, appeared in all 82 games for the Florida Panthers last season, recording 16 goals and 46 points.
The hockey legend sits second on the NHL's all-time points list with 1,914, and third in goals with 765 - 36 behind Gordie Howe. He could also achieve another career milestone with the Flames.
Jagr joins the Flames after speaking with the St. Louis Blues, who reached out to the Czech winger following a season-ending injury to Robby Fabbri. Jagr ultimately rejected the Blues' offer, saying he was going in a different direction, which we now know is north to Alberta.
Amazingly, he joins a Flames club that features Matthew Tkachuk, whose father, Keith, was selected 19th overall at the NHL Draft in 1990 - 14 spots after Jagr.