Rikaby, a liberal Islamist, returned to Iraq briefly after the 2003 U.S.-led invasion but refused to stay in protest of what he described as postwar corruption and lack of justice to the victims of the deposed Ba'athist government.
His family says he died of heart disease on 11 December, aged 72.
A wealthy Baghdad merchant and landowner, Rikaby financed opposition groups inside and outside Iraq. Although he shared a prison cell with Saddam Hussein in 1964, he opposed the Ba'ath Party long before it came to power a few years later.
Rikaby also built regional contacts. In 1988 he was one of the first outside witnesses to enter Halabja after Iraqi forces hit the Kurdish town with chemical weapons, killing thousands.
Saddam Hussein In Pictures
A slideshow of photographs from Saddam Hussein's years ruling Iraq through his downfall.