Sir Vince Cable and past Lib Dem leaders joined Theresa May, Jeremy Corbyn and others including Tony Blair in hailing the dedication and decency of the politician and former commando, who passed away on Saturday evening.
The former party leader, who was credited with making the Lib Dems a significant third force in politics during his tenure between 1988 and 1999, had announced he was suffering from bladder cancer in November.
The party announced his passing, saying he would be remembered "as someone who made an immeasurable contribution to furthering the cause of liberalism".
Sir Vince Cable, the party's current leader, said it was "a hugely sad day" for the party and everyone else across politics "who had immense affection and respect for Paddy".
He hailed a man who "was famous for his politics, but his talents extended well beyond that arena".
Born in India and raised in Northern Ireland, he later served in the Royal Marines and Special Boat Service, including in Borneo and the Persian Gulf.
He hit the headlines four years into his leadership of the Lib Dems when, in 1992, he revealed he had had a five-month affair with his secretary, which led The Sun to nickname him "Paddy Pantsdown".
His marriage to wife Jane survived the scandal.
He became High Representative for Bosnia and Herzegovina in May 2002 and, more recently, went on to play a role in the Remain campaign during the 2016 referendum, appearing alongside then-PM David Cameron and Lord Kinnock, the former Labour leader.
After revealing his cancer diagnosis, he tweeted that it "does not merit a fuss", adding: "Many go through this. The NHS guys in Yeovil Hosp. are BRILLIANT.
"I have the best of people and the best of friends to fight this with, which makes me, as so often in my life, very lucky."
Sir Nick Clegg, who would as leader take the Liberal Democrats into government in 2010, said Lord Ashdown had been "the reason I entered politics" and became "a lifelong mentor, friend and guide".
He added: "He was a soldier, a diplomat, a writer, a leader, a campaigner, a servant of his constituents, and an international statesman.
"But the thing I admired most in him is that rarest of gifts - a politician without an ounce of cynicism."
Former Labour prime minister Tony Blair said he admired the former Lib Dem leader "as a man and as a political visionary and leader", saying he had been "excellent company, always fun to be around".
And Mr Blair's successor Gordon Brown described Lord Ashdown as "one of the towering political figures of our generation who spoke always as a strong European, a committed internationalist and a dedicated constitutional reformer".
Archbishop of Canterbury, Justin Welby, hailed Lord Ashdown's work in Bosnia, saying: "Paddy Ashdown was an advocate for those others forgot, full of courage, integrity and immensely gifted.
"He served the people of the Balkans with passion and inspiration, an agent of reconciliation."
Current Prime Minister Theresa May said Lord Ashdown had "served his country with distinction", adding: "He dedicated his life to public service and he will be sorely missed."
Former Tory international development secretary Andrew Mitchell, who worked with him during the coalition years, said Lord Ashdown had been "a wonderful man and a hugely effective politician" who had been admired by Margaret Thatcher.
Mr Mitchell told the Press Association: "He was an extraordinary character. Mrs Thatcher had immense respect for him and although he was a political opponent, held his views in the highest regard."