Kabbah, who led the country during an 11-year conflict in which thousands had their limbs hacked off and 120,000 people were killed, was at home when he was pronounced dead, said John Benjamin, a family friend and former chairman of Kabbah's party.
The government of President Ernest Bai Koroma led tributes to Kabbah, describing him as "one of the pillars of democracy" in the country.
"He will go down in history as one of the leaders who stood tall in ensuring that he shook hands with people that were rejected by the majority of Sierra Leoneans during the war," government spokesman Abdulai Bayraytay told reporters.
Bayraytay said Koroma would cut short a visit to Congo-Brazzaville to return to Freetown tomorrow and pay his respects.
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Kabbah was praised for launching a disarmament programme that led to the official end of the war in January 2002 with the help of a United Nations peacekeeping force and British military trainers.
He was also praised for maintaining stability until he stepped down in 2007, although his presidency was also marked by criticism of his failure to lift what was then the world's second poorest country out of poverty.
Born in February 1932 to a Muslim family in eastern Sierra Leone, Kabbah received a Christian education and married a Catholic, who died in 1998.
After studying human sciences in Britain, he joined the civil service in 1959.
After the SLPP was defeated in elections in 1968, Kabbah lost his job and all of his property was confiscated. He then left for Britain where he studied law and became a jurist.
In 1992, a year after the rebel Revolutionary United Front (RUF) launched a particularly bloody insurrection, Kabbah quit the UN and was named president of a national consultative council.