Born Jean-Baptiste Ndahindurwa, King Kigeli came to power in 1959 and was forced to leave the country the following year after clashing with the Belgian colonial power. In 1961, the monarchy was abolished.
The king began a life of exile in east Africa, including Kenya and Uganda, before leaving for America, where he settled in the suburbs of Washington in 1992.
"It is with a very heavy heart that we announce that His Majesty King Kigeli V Ndahindurwa, the last King of Rwanda, died early this morning," read a statement on his website.
"He was a devout and dedicated believer and the last anointed African Roman Catholic king to reign over a full country."
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Funeral arrangements, and details on the heir to the throne will be announced at a later date, the statement said.
King Kigeli had come to power after succeeding his half- brother Mutara III, who died in unclear circumstances on the eve of the Hutu "social revolution" which sent hundreds of thousands of ethnic Tutsi fleeing.
Kigeli V is a Tutsi, but the tradition is that the monarchy represent all Rwandans of all ethnicities.
In September 1961, the monarchy was abolished by referendum and Rwanda gained independence the following year.
While in the United States, the exiled monarch led the King Kigeli V Foundation to aid Rwandan refugees.
A 2013 profile in Washingtonian magazine, found him living in subsidised housing, on food stamps and donations, in Oakton, Virginia, happy to hand out chocolates to neighbors' children.
For decades he spoke of returning to his east African homeland -- a tiny, landlocked country that ranks among the world's poorest nations -- but as monarch.
Since 1994 and the rise to power of current President Paul Kagame's Rwandan Patriotic Front (RPF) -- which emerged from a former Tutsi rebellion -- the issue of a potential return by the king was regularly brought up.
Yet every effort failed: the RPF authorities have always said they were ready for him to return, yet only as a private citizen. The former monarch held out hope he could return to the throne.