After protracted negotiations, Bill Nicholson signed Greaves for Tottenham Hotspur in December 1961 for £99,999 – the unusual fee was intended to relieve Greaves of the pressure of being the first £100,000 player in British football. He joined Spurs just after they became the first club in England to complete the First Division and FA Cup double during the 20th century. He played his first game in a Spurs shirt for the reserve team on 9 December 1961, and scored twice in a 4–1 win over Plymouth Argyle Reserves at Home Park. He scored a hat-trick on his first team debut, including a flying scissor kick, in a 5–2 win over Blackpool at White Hart Lane. He went on to feature against Benfica in the semi-finals of the European Cup; in the first leg at the Estádio da Luz he had a goal disallowed for offside, and another disallowed in the return fixture also for offside. He played in all seven games of the club's FA Cup run, scoring nine goals in the competition as they beat Birmingham City (after a replay), Plymouth Argyle, West Bromwich Albion, Aston Villa and Manchester United to reach the 1962 FA Cup Final against Burnley at Wembley. Greaves opened the scoring against Burnley on 3 minutes when he hit a low shot past goalkeeper Adam Blacklaw from a tight angle, and Spurs went on to win the game 3–1. They finished the league in third place in 1961–62, four points behind champions Ipswich Town.