A statement said the ex-Manchester United and Northern Ireland star died on Friday afternoon following "a long and very valiant fight".
Best had multiple organ failure after a lung infection which he developed last week led to internal bleeding.
He had been in west London's Cromwell Hospital since being admitted with flu-like symptoms on 1 October, later suffering a kidney infection.
Best, a recovering alcoholic, needed drugs after a 2002 liver transplant that made him susceptible to infection.
The Belfast-born former footballer and television pundit had been prescribed medication to suppress the immune system and prevent his body rejecting the new liver.
At the time of his hospital admission in October, Best's agent Phil Hughes said his client had been "off the drink" before being admitted to the hospital.
Best is widely regarded as one of the greatest players to have graced the British and world game.
His heyday occurred during the 1960s, and he brought a pop star image to the game for the first time.
But the accompanying champagne and playboy lifestyle degenerated into alcoholism, bankruptcy, a prison sentence for drink-driving and, eventually, his controversial liver transplant.
He helped Manchester United win the First Division title in 1965 and 1967 and the European Cup in 1968. His role in the team's success was recognised by his becoming the European Footballer of the Year in 1968.
Best made 466 appearances for the Old Trafford club, scoring a total of 178 goals.
He also won 37 caps - scoring nine goals - for Northern Ireland.
