White, 26, played only 43 regular-season games with Calgary after the Flames obtained him in the Jan. 31 multi-player deal that saw former Norris Trophy finalist Dion Phaneuf sent to Toronto. He had two goals and four assists in 16 games this season after posting 13 goals and 25 assists last year.
Sutter, meanwhile, is the 23-year-old son of Flames General Manager Darryl Sutter. He was traded only days after being arrested after an alleged bar fight in Arizona, the Canadian Broadcasting Corp. reported.
Kostopoulos, 31, has played previously in Pittsburgh, Los Angeles and Carolina, and Babchuk, 26, has scored 26 goals and 43 assists in 185 NHL games.