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 1970 season, and seemed well on his way to stardom.

Halfway through the next season he was traded to the Red Wings in a major deal (sending superstar Frank Mahovlich to Montreal). His promise of stardom was fulfilled the season following, when he scored 42 goals on a line centered by veteran star Alex Delvecchio.

In the next season, 1972-1973, Redmond exploded, becoming the seventh player in NHL history to score fifty goals in a season. He finished with 52 goals, surpassing Gordie Howe's team record, which would stand until John Ogrodnick broke it in 1985, and achieved his career high point total with 93. Delvecchio retired early in the 1973-1974 season to become the team's coach, but Redmond was moved onto a line with budding superstar Marcel Dionne. His success continued, becoming only the third player to have back-to-back fifty-goal seasons with 51 and leading the NHL in power play goals with 21.

In the 1974-1975 season, however, he sustained a back injury and played only 29 games. His back woes continued the following year, robbing him of effectiveness, and after 37 games, he retired early at the age of 28. He had been named to the league's First All-Star Team in 1973, the Second Team in 1974, and he played in one All-Star Game.

After his playing career ended, Redmond became a popular color analyst for the Detroit Red Wings. His no-nonsense opinionated style (reminscent of Don Cherry on CBC), colorful language ("Bingo Bango!", "this is what the fans came for!", "this is no place for a nervous person"), and history with the team made him a local celebrity.

Redmond's brother Dick was an NHL defensemen. He played thirteen seasons, primarily with the Chicago Blackhawks and the Boston Bruins.