Contract terms were not disclosed on Friday but Murphy's salary will be determined by whether he plays for the Devils or one of their minor league affiliates.
Murphy split last season with Florida, Rochester in the AHL and Tampa Bay. He had five goals and 11 assists in 32 NHL games. He was claimed off re-entry waivers by the Lightning in January after starting the season with the Panthers.
Murphy, who spent six seasons playing in Europe, added two goals and four assists in five AHL appearances.