His death is not being treated as suspicious and the cause of his death has yet to be confirmed.
The ex MP lost his seat in the Ross, Skye and Lochaber constituency to SNP's Ian Blackford in last month's general election.
His shocked family paid tribute to the politician yesterday:
'It is with great sadness, and an enormous sense of shock, that we announce the death of Charles Kennedy.
'Charles died at home in Fort William yesterday. He was 55. We are obviously devastated at the loss.
'Charles was a fine man, a talented politician, and a loving father to his young son. We ask therefore that the privacy of his family is respected in the coming days.
'There will be a post-mortem and we will issue a further statement when funeral arrangements are made.'
A spokesman for Police Scotland 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 and our report will be submitted to the procurator fiscal.'