One of England's greatest forwards, Greaves scored 44 goals in 57 international appearances and is Spurs' record goal-scorer with 266 goals in 279 games.
Greaves also played for AC Milan and West Ham United and scored a total of 366 top-flight goals during a 14-year career, which stood as a record for most goals scored in Europe's top five leagues for 46 years until it was broken by Cristiano Ronaldo in 2017.
A member of England's 1966 World Cup-winning squad, Greaves missed out on the final after getting injured during the tournament. He was replaced by Geoff Hurst, who scored a hat trick in England's 4-2 win against West Germany.
RIP Jimmy Greaves. A true legend and one of the great goalscorers. Thoughts are with his family and friends. pic.twitter.com/YYyLdeUHXi— Harry Kane (@HKane) September 19, 2021
Alcoholism cut Greaves' career short at the age of 31, and he also had health issues during his later years and suffered strokes in 2012 and 2015.
Gary Lineker, a former Tottenham and England striker, said: "Terribly sad news that Jimmy Greaves has died. Quite possibly the greatest striker this country has ever produced. A truly magnificent footballer who was at home both in the box and on the box. A charismatic, knowledgeable, witty and warm man. A giant of the sport."
England manager Gareth Southgate said the national team would pay tribute to Greaves in next month's World Cup qualifier against Hungary at Wembley, while Spurs and Chelsea also paid tribute to their former player.
"Jimmy Greaves was someone who was admired by all who love football, regardless of club allegiances," Southgate said in a statement released by the Football Association.
"I was privileged to be able to meet Jimmy's family last year at Tottenham Hotspur as the club marked his 80th birthday. My thoughts are with them and I know the entire game will mourn his passing."
Born in east London in 1940, Greaves signed for Chelsea and made his professional debut at the age of 17. He scored 132 goals in 169 games, racking up 100 league goals by the time he turned 20.
He attracted interest from Italy and signed with AC Milan in 1961, but only managed 12 appearances and nine goals in his single season at the club.
We are deeply saddened to learn of the passing of Jimmy Greaves at the age of 81.— England (@England) September 19, 2021
Jimmy was part of our @FIFAWorldCup-winning squad and scored a remarkable 44 goals in 57 games for the #ThreeLions.
All of our thoughts are with his family, friends and former clubs. pic.twitter.com/CetXiwD25l
Greaves returned to England with Spurs in 1962 for £99,000 and scored in the FA Cup final as Tottenham lifted the trophy that season.
His nine seasons in north London coincided with the most successful decade in the club's history. Greaves would also win the FA Cup with Spurs in 1967, as well as the European Cup Winners' Cup in 1963.
Greaves made his England debut in 1959, scoring in a 4-1 win against Peru. He holds the record for the most hat tricks scored by an England player and netted the first of his six in an 8-0 win against Luxembourg in 1960.
He scored the last of his 44 England goals in 1967 and is fourth on England's all-time goal-scorers list behind Wayne Rooney, Bobby Charlton and Gary Lineker.
After leaving Spurs in 1969, Greaves moved across London to sign for West Ham, where he stayed for two seasons until 1971. Due to alcoholism and fitness issues, Greaves was less prolific during his final two years in the top flight and scored 13 goals in 40 appearances for West Ham before he retired in 1971 at the age of 31.
After retiring, Greaves pursued a career in broadcast media and presented popular football talk show "Saint and Greavsie" alongside former Liverpool striker Ian St John from 1985 to 1992.
Greaves eventually received his World Cup winners medal in 2009. Due to FIFA rules which were subsequently overturned, only the players who finished England's 4-2 win over West Germany on the pitch received winners' medals in 1966.