Akii-Bua, a senior superintendent in the Ugandan police force, won the 400 metres hurdles at the 1972 Munich Olympics in 47.82sec, a record which stood for the following four years.
Akii-Bua died on Friday, a week after he was admitted to hospital with abdominal pains. He was 49 and had been ill for some time, athletics officials said.
He was a native of Lango, northern Uganda, where the local sports stadium is named after him. A road in Kampala was also named after Akii-Bua by Idi Amin, who ruled Uganda at the time of Akii-Bua's gold medal.
Amin also gave him a house in Kampala but Akii-Bua fled from Uganda in 1979, the year in which Amin was ousted. He was one of thousands of Ugandans, many of them from northern districts, who went when anti-Amin forces took over He did not return until 1987.
Akii-Bua is survived by a wife and 11 children. He came from a polygamous family, one of 50 children his father had by nine different mothers.
Government officials said on Sunday a decision would be taken whether to give Akii-Bua national hero status for his achievement on the track and whether to accord him a ceremonial funeral.