Amin, who was responsible for the deaths of hundreds of thousands of his countrymen, had been on a life-support machine since July 18th.
The one-time darling of the British army was thought to be 78.
Having suffered kidney failure, Amin passed into a coma and was admitted to the King Faisal Specialist hospital in Jeddah, Saudi Arabia, where he lived. He died on Saturday morning and was buried in the Red Sea coastal city.
Amin had thousands of enemies, many of whom were not saddened by the news of his death. "Good," responded a spokesman for the current Ugandan President, Mr Yoweri Museveni. "His death signals the end of our bad past."
The Rt Rev Dr John Sentamu, the Anglican Bishop of Birmingham, called it a "tragedy" that Amin was not brought to justice.
The Church of England's first senior black bishop fled Uganda in 1974 after suffering life-threatening injuries in an attack by Amin's henchmen.
The former lawyer and judge said: "I worked as a member of the Ugandan bar and the bench during Amin's reign of terror.
"I faced considerable challenges upholding the law in the north of the country, where Amin murdered many men, creating widows and countless orphans.
"I was arrested and beaten up by Amin's hit squad, eventually leading to medical complications and internal bleeding which subsequently became life-threatening."
The bishop, now in his 50s, added: "A dictator who escaped the law was never brought to justice to face his victims and given a chance to ask for forgiveness and make reparation." The bishop also helped the Ugandan Asians who were stripped of their possessions and exiled from the country.
In 1972, Amin made headlines around the world when he expelled some 40,000 Asians - descendants of migrants from the British Empire in India - saying God had told him to transform Uganda into "a black man's country".
Mr Manubhai Madhvani fled Uganda in 1972, losing everything, but rebuilt his trading empire in the UK. It was valued at 190 million in 2001.
In an interview he said: "In 1972, I was imprisoned by Idi Amin for being a brown Asian businessman in Uganda." Amnesty International was also unhappy that Amin had not paid the price for his crimes.
"Amin's death is a sad comment on the international community's inability to hold leaders accountable for gross human rights abuses," spokesman Mr George Ngwa said.
Amin was a well-known figure in the British military and began his career in the King's African Rifles of the British colonial army in 1946. He rose through the ranks to lieutenant and was one of only two native Ugandans to receive a commission from the British army during colonial rule.
In January 1971, the one-time heavyweight boxing champion staged a successful coup while President Milton Obote was out of the country. Relations soon soured between the UK and Uganda.
In 1975, Amin wrote to the queen: "My dear queen. I would like you to arrange for me to visit Scotland, Ireland and Wales to meet the heads of revolutionary movements fighting against your imperialist oppression." He is also reported to have sent her a telex which read: "Dear Liz, if you want to know a real man, come to Kampala."
During eight years of tyrannical rule, Amin ordered the execution of hundreds of thousands of Ugandans from rival tribes.
Uganda remains full of stories of how Amin kept severed heads in a fridge, fed corpses to crocodiles and had one of his wives dismembered. Some say he practised cannibalism.
Estimates put the number of those murdered by Amin in the east African state at more than 100,000.
The dictator was a large and imposing figure who revelled in publicity, and his eccentric behaviour created the image of a buffoon given to erratic outbursts.
He declared himself king of Scotland, banned hippies and miniskirts, and attended a Saudi royal funeral wearing a kilt.
In 1979, forces from neighbouring Tanzania and Ugandan exiles drove Amin from power and Obote returned.
Saudi Arabia gave Amin sanctuary in the name of Islamic charity. He lived quietly in Jeddah with four wives on a government stipend.
In a rare interview in 1999, Amin told a Ugandan newspaper he liked to play the accordion and recite the Koran.