Kennedy, whose party were virtually wiped out at last month’s general election after five years in coalition with Prime Minister David Cameron’s Conservatives, led the party from 1999 to 2006.
“Charles’s untimely death robs Britain of one of the most gifted politicians of his generation,” Nick Clegg, former Liberal Democrat leader and deputy prime minister until May’s election, said in a statement.
Kennedy, who had a wife and 10-year-old son, died on Monday. The cause of his death was not given and the family statement said a post-mortem examination would take place.
Kennedy was first elected to parliament in 1983, when he defeated a government minister to become the youngest member of parliament at the time. He lost his seat to the Scottish nationalists at last month’s election.
Mr Kennedy led the Liberal Democrats to their best general election result before or since, in 2005, when they gained 62 seats.
Much of his party’s popularity at the time was gained by Mr Kennedy’s decision to oppose the war in Iraq.
He was the only Liberal Democrat MP to vote against the formation of the coalition in 2010.
Tributes poured in for Mr Kennedy from senior figures from across the political spectrum.
In a statement outgoing party leader Nick Clegg said: “Charles’s untimely death robs Britain of one of the most gifted politicians of his generation.
“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,” he said.
“He was a staunch internationalist and passionate believer in Britain’s role in Europe, yet he was a proud Highlander, Scot and British parliamentarian.
“He was one of the most gentle and unflappable politicians I have ever known, yet he was immensely courageous too not least when he spoke for the country against the invasion of Iraq.
“He led the Liberal Democrats to our party’s greatest electoral successes, yet he always remained modest about his huge achievements.
“Whenever I asked him for advice, he was unfailingly kind and wise,” the former deputy prime minister added.
“Most of all, I will never forget the pride and love with which he would talk about his own family, most especially his devotion to his son Donald.
“My heart goes out to his sister and brother and to Sarah and Donald at this tragic time.”
Former Lib Dem leader Paddy Ashdown has described Charles Kennedy’s death at the age of 55 as “a loss to the whole of British politics”.
Mr Kennedy was a man who brought decency, principle, judgement, charm and wit to the Commons, he said.
“When he was on song Charles was the best of all of us,” he added.
Despite losing his parliamentary seat last month, Kennedy had hoped to be actively engaged in what he called “the great European debate which is now looming”. Cameron has promised a referendum on Britain’s EU membership by the end of 2017.
“The next few years in politics will come down to a tale of two Unions the UK and the EU. Despite all the difficult challenges ahead the Liberal Democrat voice must and will be heard,” Kennedy wrote after his electoral defeat.