A winger, Morgan started his career with
Burnley, making his first-team debut against
Sheffield Wednesday at
Hillsborough in 1963. He took over from
John Connelly who was transferred to Manchester United and scored his first Burnley goal, when he scored twice in a Boxing Day demolition of Manchester United in a 6–1 win at
Turf Moor. He made his
Scotland debut against
Northern Ireland at
Belfast's
Windsor Park in 1967. He was transferred to
Manchester United early in the 1968/9 League season, after Utd's John Aston had broken a leg. He scored 34 goals for United and led them to promotion in 1975 after one season in the Second Division. He played in the World Cup Finals of 1974, which took place in West Germany. With
Steve Coppell's signing in 1975, Morgan lost his place in the Manchester United team and returned to Burnley. His second spell at
Turf Moor lasted less than a year. He moved to
Bolton Wanderers, enjoying a successful spell at
Burnden Park before finishing his career at
Blackpool. Morgan played summers on loan in the
North American Soccer League in the late 1970s, playing for the
Chicago Sting in 1977 and
Minnesota Kicks the following three summers. During his time at Manchester United, the band Tristar Airbus, a pseudonym for the future members of
10cc, recorded the song "Willie Morgan" in tribute to the footballer. It would later appear on the compilation
Strawberry Bubblegum: A Collection of Pre-10CC Strawberry Studio Recordings 1969–1972. ==International career==