Henning has won four Stanley Cups, two as a forward for the New York Islanders and two as an assistant coach. He played nine NHL seasons, all with the Islanders, before transitioning behind the bench as an assistant coach for the Islanders. He served as an Islanders assistant for nine seasons, spanning two stints, and also took over as head coach for parts of three NYI seasons. He was the head coach of the Minnesota North Stars (now the Dallas Stars) for two seasons. He added five more years as an NHL assistant in Chicago and Anaheim before moving on to front-office roles, most recently with the Montreal Canadiens.

He assisted on New York Islanders teammate Bob Nystrom's famous May 24, 1980, goal that won the first of four straight Stanley Cups for the Islanders' 1980s dynasty.