Asham, a physical player who is considered an underrated shooter, had 10 goals, 14 assists and 126 penalty minutes for Philadelphia last season, playing mostly on the fourth line.
Asham had four goals and three points in 23 playoff games as the Flyers reached the Stanley Cup finals.
The 10-year NHL veteran played previously for Montreal, the Islanders and New Jersey. He has 82 goals and 97 assists in 648 games. His career high was 15 goals with the Islanders in 2002-03.