Born Eric Lubbock, he became Liberal MP for Orpington in 1962 when he won a by-election with a huge 22% swing from the Conservatives.
He held the seat for eight years, moving to the Lords in 1971 when he inherited the title of Baron Avebury.
Lib Dem leader Tim Farron paid tribute to a "true Liberal", "great campaigner" and "committed internationalist".
Lord Avebury: Obituary
Mr Farron  said the peer, who had been suffering from leukaemia, would "be remembered as much for his unyielding commitment to fighting for Liberal causes as his sensational by-election victory".
"He campaigned to lower the voting age, founded the parliamentary human rights group and fought for the rights of refugees and asylum seekers, taking up the cases of hundreds of individuals fleeing persecution.
"He was a committed internationalist, regularly promoting human rights around the world. The Liberal Democrats have lost a great campaigner, a great friend and a true champion of the Liberal cause."
A Buddhist, Lord Avebury was the patron of Angulimala, which promotes the teaching and practice of Buddhism in British prisons.
He also campaigned on behalf of secular causes, fighting to remove mandatory daily worship in maintained schools.
In 2009, the National Secular Society named the peer secularist of the year, jointly with Evan Harris, for his work on abolition of blasphemy laws in England and Wales.
His biography on the Lib Dem website says he also "sought and won" a battle with the senior parliamentary official known as Black Rod to keep the right to park bicycles against the front of the Houses of Parliament.
Keith Porteous Wood, executive director of the National Secular Society, said Lord Avebury had supported countless human rights campaigns.
"His knowledge of foreign affairs, particularly of remote parts of the developing world, was second to none. The weak and oppressed in these places have lost a true champion.
"I have lost a very close friend. The nation has lost a human rights champion."
The longest-serving Lib Dem peer and veteran human rights campaigner, Lord Avebury, has died at the age of 87.