Green, known as "Terrible Ted" for his physical style of play, was born in St. Boniface, Manitoba, on March 23, 1940. He was originally the property of the Montreal Canadiens but was claimed by the Bruins in the NHL intraleague draft on June 8, 1960. Green made his NHL debut with Boston against the Detroit Red Wings on Nov. 10, 1960, before being returned to junior hockey, and became a regular with the Bruins the following season.
He had more than 100 penalty minutes in each of his first five NHL seasons, but when Boston improved in the late 1960s, Green's skills became more apparent. He was voted an NHL Second-Team All-Star in 1968-69 after finishing with an NHL career-high 46 points (eight goals, 38 assists).
However, Green missed all of the Bruins' run to the Stanley Cup in 1970 after being hit in the head with a stick during a preseason game, although his name was engraved on the Cup.
Green returned in 1970-71 and was a member of Boston's Cup-winning team in 1971-72 before signing with the New England Whalers of the new World Hockey Association. He played three seasons with the Whalers and four with the Winnipeg Jets, winning three championships, before retiring in 1979. Green had 254 points (48 goals, 206 assists) in 621 NHL games, as well as 12 points (four goals, eight assists) in 31 playoff games.
After retiring, Green joined the Oilers and was an assistant under former Bruins teammate Glen Sather during their run of five Stanley Cup championships from 1983-84 through 1989-90. He was a co-coach with the Oilers in 1990-91 and was named coach for the 1991-92 season. The Oilers went 65-102 with 21 ties under Green until he was fired after Edmonton started 3-18 with three ties in 1993-94.
Green returned to the Oilers as an assistant in 1997 and spent three seasons with Edmonton before joining the Rangers.