The 35-year-old left wing had 56 goals, 52 assists and 561 penalty minutes in 524 career games.
Begin played 159 games with the Flames and was in his second stint with the team. He began his career with Calgary from 1997 to 2003, and then rejoined the Flames as a free agent for the 2012-13 campaign after taking the previous season off due to a hip injury.
He again attempted to continue his career with the Flames this season but decided on retirement after a reoccurrence of the hip injury during training camp.
Begin also played with Montreal, Dallas, Boston and Nashville.