The 28-year-old centre signed a US$16-million, four-year deal with Calgary on the second day of NHL free agency.
It will be just the second NHL team for Hudler.
In 409 career games, all with Detroit, he had 87 goals and 214 points. He scored 25 goals and 50 points in 81 games for the Red Wings last season.
"He is one of the very best goal scorers in the NHL at even strength," said Flames general manager Jay Feaster.