The former England striker, who also played for Chelsea, West Ham and AC Milan, suffered a stroke in May 2015 which left him wheelchair-bound and with severely impaired speech.
Spurs said he died in the early hours of Sunday morning.
His passing was announced on the club’s website in a statement paying homage to his remarkable goal-scoring feats.
“We are extremely saddened to learn of the passing of the great Jimmy Greaves, not just Tottenham’s record goalscorer but the finest marksman this country has ever seen,” read Tottenham’s statement.
Gifted with rare pace and poise, Greaves scored 266 goals in 379 appearances for Spurs between 1961 and 1970, including 220 goals in 321 league games, 32 goals in 36 FA Cup ties, five in just eight League Cup ties and nine in 14 European matches.
The 37 league goals that he netted in the 1962/63 season remains Tottenham’s record by any player in a single season.
A member of England’s 1966 World Cup-winning squad, Greaves also scored 44 goals in his 57 senior international appearances – including six hat-tricks – with 42 of those caps and 28 goals won while a Spurs player.
He was bitterly disappointed after missing the World Cup Final with a gash to his shin, having played a leading role for Sir. Alf Ramsey’s side in the rest of the tournament.
His replacement, Sir. Geoff Hurst, scored a hat-trick in the 4-2 victory over West Germany at Wembley.
Born in East Ham on 20 February, 1940, Greaves’s career started in the junior ranks at Chelsea where he turned professional in May, 1957.
He scored on debut, ironically against Tottenham at White Hart Lane on August, 24, 1957, in a 1-1 draw.
He remained at Stamford Bridge until June, 1961, when he moved to AC Milan, and his 41-goal haul in the First Division in 1960/61 still stands as Chelsea’s record for a single season.
He soon moved to Tottenham and scored on debut against Blackpool on 16 December, 1961, bagging a hat-trick to give an indication of what was to follow during the course of the next nine years.
Tottenham’s statement continued: “Although we had just won the ‘Double’, there’s no question that Jimmy’s arrival in N17 made us an even better team.
“He was a natural goalscorer, always in the right place at the right time to add the finishing touch to another well-worked move, while he could also create his own goals, as he did on numerous occasions by gliding past defenders and passing the ball into the back of the net.
“He possessed immaculate ball control, great balance and such composure in front of goal that he rarely spurned an opportunity.”
His brace in the European Cup Winners’ Cup Final helped Tottenham to a 5-1 demolition of Atletico Madrid, as Spurs became the first British club to win a European trophy.
When he topped the First Division goalscoring charts in 1964/65 with 29 goals, he became the first player to do so in three consecutive seasons and he broke the 20 league goals barrier in three other campaigns for the club.
His final honour came in the 1967 FA Cup Final, playing his part in a 2-1 win over his former club Chelsea.
He left Spurs in March, 1970, to join West Ham United, before retiring at the end of the 1970/71 season at the age of 31.
In October, 1972, a crowd of 45,799 gathered at White Hart Lane to pay tribute to him in his testimonial match against Feyenoord.
Following a spell at West Ham, Greaves retired as a player in 1980 and went on to become one of the nation’s best-loved TV pundits as one half of Saint and Greavsie, a popular weekend football show which he presented alongside former Liverpool and Scotland striker Ian St John.
Missing the World Cup Final and the death of his four-month-old son, Jimmy Jnr., in 1961 contirbuted to the alcoholism that Greaves battle for years in the latter part of his playing career and following his retirement.
He was awarded an MBE in the Queen’s New Year Honours list at the end of 2020.
Spurs legend, Glenn Hoddle, who grew up watching Greaves on the terraces of White Hart Lane, tweeted: “Such sad news this morning on Jimmy s passing. A true legend of the game , love and thoughts to all of Jimmy’s family. R.I.P”