The addition of Brent pushes the total number of Sutters in the Flames organization to five.
Brother Duane is director of player personnel, brother Ron is a scout and Darryl's son Brett played for the Flames farm team last season.
Mike Keenan was fired as coach of the Flames on May 22.
Darryl Sutter said there were three key things he considered when choosing his new coaching staff.
"Number one was leadership, (that was) very, very important," he said during a news conference. "Number two was structure and number three was detail."
"There was some personal things that he understood," Brent said of Devils general manager Lou Lamoriello, who was elected to the Hockey Hall of Fame on Tuesday.
Brent Sutter coached the Devils to a 97-56-11 regular-season record in his first two seasons as an NHL coach, but New Jersey was upset in the first round of the playoffs in both seasons.
The Flames underachieved last season with a fourth straight exit in the first round of playoffs. Calgary led the Northwest Division by 13 points in January, but injuries and inconsistent play eroded that cushion and cost Calgary home-ice advantage in the postseason. The Flames finished fifth in the Western Conference with a 46-30-6 record.