Law's career as a football player began at Second Division Huddersfield Town in 1956. After four years at Huddersfield, Manchester City signed him for a transfer fee of £55,000, setting a new British record. Law spent one year there before Torino bought him for £110,000, this time setting a new record fee for a transfer between an English and an Italian club. Although he played well in Italy, he found it difficult to settle there and signed for Manchester United in 1962, setting another British record transfer fee of £115,000.
He is best known for the eleven years that he spent at United, where he scored 237 goals in 409 appearances and was nicknamed The King and The Lawman by supporters. He is the only Scottish player in history to have won the prestigious European Footballer of the Year award, doing so in 1964, and helped his club win the First Division in 1965 and 1967. Law left Manchester United in 1973 and returned to Manchester City for a season, then represented Scotland in the 1974 FIFA World Cup. Law played for Scotland a total of 55 times and jointly holds the Scottish international record goal tally with 30 goals. Law is also United's second highest goalscorer behind Bobby Charlton. Law holds a United record for scoring 46 goals in a single season.