The controversial but popular scheme allowed people to travel anywhere in the county for 10p, or for free in Sheffield.
Mr Waugh and fellow county councillors John Cornwell, Roy Thwaites and David Blunkett now a Sheffield MP and former Home Secretary, were instrumental in pushing through the policy which was an attempt to tackle environmental issues and congestion by encouraging people onto the buses.
He was also involved in the introduction of Bendibuses to Britain and Sheffield’s supertram network.
The cheap fares policy continued despite opposition from the Conservative government of Margaret Thatcher and its withdrawal of the transport grant in a bid to stop it. But Mr Waugh stuck with it until the end when South Yorkshire County Council was abolished in 1986 along with all the other metropolitan county councils.
Paying tribute to him Mr Blunkett said: “A small group of us who were at that time in the early 1970s on South Yorkshire County Council and Sheffield City Council developed the South Yorkshire transport policy which became internationally renowned.
“We should remember him for a tremendous contribution to the wellbeing of local people and to cutting-edge policies which attracted attention across the world.”
Alexander Waugh was born in Kirkcaldy and had a brother Robert, and sister Rosabelle who died in a motorcycle accident aged 19. Their father James was a draughtsman and college lecturer, and their mother Betty a school secretary.
After leaving school, he served an apprenticeship as a compositor before serving National Service in the RAF.
In 1960, he went to Dudley Training College to study to become a teacher and on leaving in 1963 lectured at Walsall Technical College.
Three years later, he moved to lecture in Portsmouth where he became active in the local Labour Party. There he won selection to stand as Labour candidate for the safe Conservative seat of Salisbury in the 1970 General Election in which he took nearly 40 per cent of the vote, but not enough to win the seat.
His political career took off when he went to Sheffield University in 1971 to do an MA in politics and he became active in local politics.
He did a survey on the changing face of the Labour Party, and then worked at Granville College in Sheffield as a lecturer in trade union studies.
In 1973 he was elected to South Yorkshire County Council for the Owlerton & Southey Green ward in preparation for it formally coming into being in 1974.
Mr Waugh was a member of the policy committee and deputy chairman of transport. He took over as chairman of transport in 1979 in succession to Mr Thwaites who, as deputy leader of the council, succeeded the leader Ron Ironmonger when he became ill.
Mr Waugh later made another attempt to find a parliamentary seat, this time in Rother Valley, but was beaten by Kevin Barron who has held the constituency since 1983.
After this, he taught economics at Netherthorpe School until retirement when he then spent much of each year travelling, mainly to France. He was a devoted follower of Sheffield United and an avid jazz fan.
Mr Waugh, who died a day before his 78th birthday, is survived by his wife Julia, three sons and five grandchildren.
A funeral service will be held at Chesterfield Crematorium on Thursday, January 16, at 12.50pm.