The 29-year-old had 11 goals and 12 assists in 80 games with the New York Islanders last season. "Arron Asham is a veteran forward who brings a level of toughness, intensity, and feistiness to our lineup," Devils chief executive Lou Lamoriello said in a statement Tuesday.
Asham has played seven seasons in the NHL - the last four with the Islanders.
He has 58 goals and 67 assists in 421 career NHL games with New York and the Montreal Canadiens.