A statement from Greaves’ family confirmed that the 75-year-old had been taken ill, having recovered from a minor stroke in 2012.
Greaves scored 44 goals in 57 England games, the fourth-highest total of all time.
He also scored 266 goals in 379 matches for Spurs.
The White Hart Lane club sent their best wishes to ‘Greavesie’, tweeting: “Everyone at the Club wishes Jimmy Greaves a speedy recovery after he suffered a stroke yesterday.’
Greaves also had spells with Chelsea - where he scored 124 goals in 157 appearances - AC Milan, West Ham, Brentwood, Barnet and Chelmsford City.
He ended his 33-year playing career at Woodford Town in 1980 following a battle with alcoholism.