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The cause of death is yet to be confirmed but it is not believed to be suspicious.
The Scottish MP lost his seat in the Ross, Skye and Lochaber constituency in last month's election.
A statement released on behalf of his family said they were "devastated" at the loss, calling Mr Kennedy "a fine man, a talented politician, and a loving father to his young son".
Police were called to his home in Fort William on Monday by paramedics to reports of the politician's "sudden death".
A spokesperson for Police Scotland said: "There are no suspicious circumstances and our report will be submitted to the procurator fiscal."
Charles Kennedy - his political career in picturesShow all 18 1 /18Charles Kennedy - his political career in pictures Charles Kennedy - his political career in pictures 1986 Charles Kennedy at the SDP conference in September 1986. He had become Britain's youngest MP three years earlier and the party later merged to become the Liberal Democrats.
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Charles Kennedy - his political career in pictures 1987 Charles Kennedy attends the Joint Liberal Assembly, October 1987.
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Charles Kennedy - his political career in pictures 1999 Charles Kennedy being congratulated by his girlfriend and future wife, Sarah Gurling, and mother Mary after being elected Lib Dem leader in 1999
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Charles Kennedy - his political career in pictures 2001 Charles Kennedy greeting supporters at a rally before the 2001 general election, when he was the Lib Dem leader
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Charles Kennedy - his political career in pictures 2002 Mr Kennedy at his wedding to Sarah Gurling, outside the House of Commons in London. The couple divorced in 2010.
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Charles Kennedy - his political career in pictures 2003 Charles Kennedy speaks during a question and answer session at the Liberal Democrat Party annual conference in Brighton
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Charles Kennedy - his political career in pictures 2004 Charles Kennedy and his then wife arrive at the British Academy Television Awards in London
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Charles Kennedy - his political career in pictures 2005 Charles Kennedy unveiling a Lib Dem campaign poster ahead of the 2005 general election
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Charles Kennedy - his political career in pictures 2005 Charles Kennedy with his then wife Sarah and new born son Donald James on 12 April 2005. He returned to the election campaign trail days later
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Charles Kennedy - his political career in pictures 2005 Charles Kennedy celebrating the Lib Dems' gains after the 2005 general election, when the party won 62 seats
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Charles Kennedy - his political career in pictures 2006 Charles Kennedy admitted his drink problem and called a leadership election in January 2006
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Charles Kennedy - his political career in pictures 2006 Charles Kennedy is canvassing in Dunfermline for a by-election a month after his resignation as Lib Dem leader
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Charles Kennedy - his political career in pictures 2006 Sir Menzies Campbell, Lord Rennard and Simon Hughes give Charles Kennedy a standing ovation after his speech to the party conference in September 2006, his first since his resignation
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Charles Kennedy - his political career in pictures 2007 Charles Kennedy and his predecessor Paddy Ashdown congratulating Nick Clegg on his election as Lib Dem leader in December 2007
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Charles Kennedy - his political career in pictures 2010 Charles Kennedy with Nick Clegg on the campaign trail ahead of the 2010 general election
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Charles Kennedy - his political career in pictures 2011 Charles Kennedy launching the pro-AV campaign for the 2011 proportional representation referendum in Glasgow
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Charles Kennedy - his political career in pictures 2014 Charles Kennedy with Danny Alexander and fellow Lib Dems campaigning for a 'no' vote in the Scottish independence referendum in 2014
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Charles Kennedy - his political career in pictures 2015 Charles Kennedy campaigning with Jo Swinson in East Dunbartonshire in April ahead of the 2015 general election, where he lost his seat
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An MP since 1983, Mr Kennedy represented Ross, Cromarty and Skye until he lost his seat to the Scottish National Party last month.
Taking over from Paddy Ashdown in 1999, he led the Liberal Democrats until his resignation in 2006.
Additional reporting by Press Association
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