Lord Greaves died unexpectedly at his home in Trawden, Lancashire, on Tuesday.
The political stalwart was a lifelong member of the liberal movement, long before the modern party was formed.
Party leader Sir Ed Davey called him a “Liberal legend”, and he said: “Lord Greaves was a bastion of local government and liberalism. His loss will be felt by all of us who believe in localism and strive for a more liberal country.”
Lord Greaves, a former teacher, was made a life peer in 2000. He was previously a Lancashire County Council councillor, and represented the Waterside ward in Colne on Pendle Borough Council until his death.
Liberal Democrat leader for the councils, David Whipp, said: "Tony was indomitable.
"His passing will leave a huge hole in the Pendle community and a similar gap in the Liberal Democrat Party nationally. His opinion was valued by people of all political parties.
"Tony had a huge love for Colne and every street in the town has been improved by his work. He was one of the inventors of Liberal Democrat community politics in the 1960s. It is very sad indeed."
In a statement, the group added: "A representative for people in Colne's Waterside ward, Tony championed the needs of Colne and its people since the days of Colne Borough Council in the 1960s, initially campaigning against the demolition of the old Colne town centre.
"Passionate and principled, Tony stood up for residents throughout over half a century of service to the people of Colne at Pendle Council and Lancashire County Council.
"In recent years, Tony became a member of the House of Lords, where he continued to campaign for the interests of local people.
"The Colne Liberal team sends its sincere condolences to Tony's wife Heather, daughters Vicky and Helen and grandson Robin.
"Not only is this a very sad day for his family, it is a sad day for Colne, too."
In an interview with The Yorkshire Post in November, Lord Greaves recalled how he first became interested in politics at Queen Elizabeth Grammar School, in Wakefield, with a group of friends.
He said: “The late 1950s, which seems like prehistoric times now, was a time for me when the Tories had been in power for quite a long time,” he said.
“Most of the 1950s in a very general sense seemed old fashioned for the day and the economy was beginning to get out of control, and the Labour Party did not seem to be very effective, it was full of internal disputes - surprise surprise, never happens now does it?
“The Liberal Party was reviving and had a particularly attractive, intelligent and charismatic leader called Jo Grimond, and we thought that it was something to attach yourself to in a very vague sort of general sort of way.”
“I actually joined in Wakefield,” he said. “And I remember it was a real coalfields pea soup. It was December and someone sold me a copy of the Liberal News and it advertised a Christmas fair, and I went along to the Methodist Hall in the middle of Wakefield and had to negotiate the street from street lamp to the next streetlamp, it was that bad, but then it was in those days.”
Describing his politics as that of a “left-wing liberal, not a socialist” Lord Graves said he still very much thought of himself as a radical.
A post from the Lib Dems in the Lords Twitter account said: “Whilst we are shocked at the suddenness of it, we remember a real Liberal hero whose contribution to local and national politics over many decades has been massive. Salutes, Tony - you will be missed.”