Greenwood played as a centre-half, joining Chelsea as an amateur whilst training as an apprentice sign-writer. During World War II he served in the Royal Air Force in Northern Ireland and guested for Belfast Celtic. In 1945, he left Chelsea for Bradford Park Avenue and made 59 league appearances over the next four seasons. In 1949, Greenwood moved to the club he supported as a boy, Brentford, his £9,500 fee breaking the club's incoming transfer record. He made 147 appearances and scored one goal. After three years at Brentford, he returned to Chelsea, where he played 66 times and won a First Division winners' medal in 1954–55 under Ted Drake. That summer, he moved to Fulham, where he made another 42 league appearances before retiring at the end of the 1955–56 season. He was never capped for his country, though he did make a single 'B' team appearance, whilst at Brentford, in a 1–0 victory against the Netherlands, on 23 March 1952, at the Olympishe Stadion, Amsterdam. At the end of his playing career in 1956, Greenwood became an active freemason attending the Lodge of Proven Fellowship No. 6225, but resigned in 1977.
Coaching career
After retiring Greenwood moved into coaching. He coached Eastbourne United, Oxford University, and England youth teams. He combined the England under-23 post with being the assistant manager at Arsenal under George Swindin, having moved to Highbury in December 1957. He remained there until April 1961, when he was selected by chairman Reg Pratt to replace Ted Fenton as manager of West Ham United. Greenwood's reign at West Ham brought them sizeable success. He oversaw the development of players such as the 1966 FIFA World Cup-winning trio of Bobby Moore, Geoff Hurst and Martin Peters, and under him the Hammers won the FA Cup in 1964 and the European Cup Winners' Cup in 1965 – the first two major trophies of their history. West Ham's league form under Greenwood was less impressive, usually finishing in the lower half of the First Division table, though they did come 6th in 1972–73. In his final season, West Ham finished 18th, just one point from relegation. He moved upstairs in 1974, becoming the club's general manager for the next three years, with John Lyall being placed in charge of the first team. In the first season of this arrangement, West Ham won another FA Cup. After England coach Don Revie's resignation, Greenwood was appointed full-time manager, ending his 16-year association with West Ham United. Under Greenwood, England qualified for UEFA Euro 1980, where they were knocked out in the group stages. England also qualified for the 1982 FIFA World Cup under Greenwood, their first World Cup in twelve years. England came through the tournament unbeaten, but were knocked out in the second group stage after 0–0 draws against West Germany and Spain. Greenwood retired from football after the 1982 World Cup, with the national coach's job going toBobby Robson. One major landmark during Greenwood's tenure was the selection of the first black player for England, Viv Anderson, in 1978. Greenwood stated "Yellow, purple or black – if they're good enough, I'll pick them".
Life after football
After his career in football Greenwood was a regular analyst on BBC Radio. He died on 9 February 2006, aged 84, after a long struggle with Alzheimer's disease. When West Ham played Birmingham City in a Premier League fixture on 13 February 2006, a one-minute silence was held in Greenwood's memory. West Ham won the game 3–0. The Town Council of Loughton, where Greenwood lived during his time as West Ham manager, erected a blue plaque to his memory on one of his former houses in the town, 22 Brooklyn Avenue: this was unveiled by Sir Trevor Brooking and the Town Mayor, Chris Pond on 28 October 2008. The Heritage Foundation charity erected a blue plaque in Greenwood's memory at West Ham's Upton Park, which was unveiled by his family on 21 January 2007. Greenwood was inducted into the English Football Hall of Fame in 2006, recognising his achievements as a manager in the English game. He is also a member of the FA and LMAHalls of Fame. He was survived by his widow, Lucy. He is buried in the Town Cemetery at Sudbury in Suffolk.