Born Jean-Baptiste Ndahindurwa, King Kigeli V came to power in 1959 but was only king of Rwanda until 1961, when the monarchy was abolished and he was forced into exile.
He eventually settled in the US where he set up a charity helping Rwandan refugees and orphans.
A 2013 profile in Washingtonian magazine found him living off food stamps in subsidised housing.
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King Kigeli was the last in a line of monarchs from the minority Tutsi ethnic group, which had dominated Rwandan for many years, but the Belgian former colonial power favoured the majority Hutus and backed a coup.
Rwanda was proclaimed a republic in 1961, and a Hutu, Dominique Mbonyumutwa, was made president.
Tens of thousands of Tutsis were forced into exile including King Kigeli, who lived the rest of his life outside Rwanda.
For three decades the country endured ethnic violence, culminating in the 1994 mass slaughter, in which some 800,000 Tutsis and moderate Hutus were killed by Hutu extremists.
King Kigeli held onto the hope that he could return to the throne in Rwanda.
A small opposition party argued that the king might be a force of unity in a country still torn by the legacy of the genocide.
As recently as May, the Democratic Green Party had requested the government to allow him to return with the benefits of a head of state, reports AFP news agency.
But without ever returning to Rwanda, King Kigeli died on Sunday morning his website announced.
"He was a devout and dedicated believer and the last anointed African Roman Catholic king to reign over a full country," it said.
It added that "the heir to the Royal throne of Rwanda" will be "announced in good order".
The last king of Rwanda has died in the US aged 80 years old.