Woosnam played football with Montgomeryshire Schoolboys and gained youth international honours with Wales, and gained eight amateur caps, the first against England in 1951. While reading Physics, he captained Bangor University's football team at the Welsh Universities' Championship. Woosnam completed his national service with the Royal Artillery. He featured for the Army XI alongside Eddie Colman and Duncan Edwards of Manchester United. He played club football at Wrexham, Manchester City, Caersws, Aberystwyth Town, and with amateur club Sutton United before he joined Leyton Orient. He made his senior international debut for Wales against Scotland in October 1958, having turned professional in January 1957. He represented the London XI against Lausanne Sports while at Brisbane Road. He was named amateur footballer of the year in 1955. In November 1958, Woosnam was signed by West Ham United for £30,000 and left his job as a physics teacher at Leyton County High School for Boys to turn professional. He made his debut against Arsenal that month and went on to make 138 League appearances for the club, scoring 26 goals. He made 15 cup appearances, scoring three goals. While at Upton Park, he added 15 full international caps to the one he had gained while at Orient. He also represented the Football League and Wales Amateurs. Woosnam moved to Aston Villa in 1962 for a £25,000 fee. He made his Villa debut on 1 December 1962 in a 5–0 home win against Bolton Wanderers. He went on to score 24 goals in 106 League games, and gained a further two international caps.
Woosnam emigrated to the United States in 1966. Although hired as a coach, he played for the Atlanta Chiefs and scored the first goal in the first football game in the Atlanta Fulton County Stadium. Woosnam became coach of the Atlanta Chiefs in 1968, and was named 'Coach of the Year' in 1968. Woosnam became head coach of the United States national team in 1968. Woosnam was Commissioner of the NASL from 1969–83. He is credited as an important factor in the development of the NASL, and had been a major figure in promoting the league and had secured TV contracts from CBS and ABC. He played a key role during 1970 in recruiting executives at Warner Communications to invest in an expansion team—the New York Cosmos. Woosnam oversaw the westward expansion of NASL in the early 1970s, establishing teams in Los Angeles, the Bay Area, Seattle, and Vancouver. However, he also guided the league into several poor business decisions, such as over-expansion to 24 teams, and the league's owners had been losing significant money and was removed from his duties as commissioner of the NASL in 1983 following a vote of the club owners. Woosnam later became managing director of the marketing arm of US Soccer, and helped bring the 1994 World Cup to the US. He was inducted into the US National Soccer Hall of Fame and the Georgia Soccer Hall of Fame in 1997.
