Greaves was a member of England’s 1966 FIFA World Cup winning squad and scored 44 goals in 57 games for the Three Lions.
He is also Tottenham’s all-time leading goalscorer, having found the net 266 times in 379 games for the North London club.
Greaves also represented AC Milan and West Ham United in his illustrious career.
A statement from Tottenham read: 'We are extremely saddened to learn of the passing of the great Jimmy Greaves, not just Tottenham Hotspur's record goalscorer but the finest marksman this country has ever seen.
'Throughout his wonderful playing career, Jimmy's strike rate was phenomenal. His Spurs return was 266 goals in 379 appearances between 1961 and 1970 – 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 statement ended: 'Football will not see his like again.'
Current and former footballers have already started paying their tributes with Tottenham and England striker Harry Kane tweeting: 'RIP Jimmy Greaves. A true legend and one of the great goalscorers. Thoughts are with his family and friends.'
Former Three Lions defender Rio Ferdinand posted: 'Big loss to the footballing world. Sending my condolences to the Greaves family. First autobiography I ever read! Inspiration.'
Arsenal legend Ian Wright commented: 'The first footballers name I ever heard from my teacher. 'No Ian! Finish like Jimmy Greaves!' May he rest in peace.'
