The Jack Button Award, given to the top prospect for the Washington Capitals, was created in his honor.
In Washington, Button was highly regarded as a scout and he was credited with discovering Peter Bondra, Jim Carey, Sergei Gonchar, Michal Pivonka and Brendan Witt.
During the 1996–97 season, the Capitals wore a memorial patch for Button which showcased his initials and a bulldog.
In 1968, the Pittsburgh Penguins appointed him general manager of their Central Hockey League affiliate, the Amarillo Wranglers.
Button is the father of Craig, a former executive with the Dallas Stars and Calgary Flames, as well as a former pro scout with the Toronto Maple Leafs.