Redmond played right wing for the Montreal Canadiens from 1967-1971, winning Stanley Cups with them in 1968 and 1969. He scored 27 goals for the Canadiens in the 1969-70 season. Halfway through the 1970-71 NHL season he was traded to the Red Wings in a deal that sent superstar Frank Mahovlich to Montreal. His promise was fulfilled the season following, when he scored 42 goals on a line centered by veteran star Alex Delvecchio. Redmond's brother Dick was an NHL defensemen. He played thirteen seasons, primarily with the Chicago Blackhawks and the Boston Bruins.