"It is with great sadness, and an enormous sense of shock, that we announce the death of Charles Kennedy," 55-year-old Kennedy's family said in a statement.
"We are obviously devastated at the loss. Charles was a fine man, a talented politician, and a loving father to his young son."
His family said they were devastated to lose a "fine man and loving father".
No cause of death has been given but police said it was not suspicious.
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Politicians including Nick Clegg and Scottish First Minister Nicola Sturgeon have been paying tribute, calling him "one of the most talented politicians".
Clegg, who resigned as Lib Dem leader last month, said: "Charles devoted his life to public service, yet he had an unusual gift for speaking about politics with humour and humility which touched people well beyond the world of politics.
A Police Scotland spokesperson said: "Police officers attended an address at Fort William on Monday, June 1 to reports of the sudden death of a 55-year-old man.
"Police were notified by ambulance service personnel. There are no suspicious circumstances.