Bergeron, 27, began last season with the New York Islanders, but was sent to Anaheim before the trade deadline. In 55 games last season, he had nine goals and 10 assists.
Over five seasons in the NHL, Bergeron had 48 goals and 80 assists in 267 games. He began his career with Edmonton in the 2002-03 season and played there until being traded to the Islanders during the 2006-07 season.
The NHL draft will be held June 20.