Mr Hayden led Labor in opposition from 1977 to 1983 before serving as foreign minister in Bob Hawke's government. He had previously served as a minister and briefly as treasurer under Gough Whitlam.
Mr Hayden went on to become Australia's 21st governor-general, holding the office between 1989 and 1996.
The prime minister led tributes to the late Bill Hayden, a former Labor leader and governor-general.
Prime Minister Anthony Albanese said Mr Hayden was a Labor legend who laid the foundations for the reforms pursued by the Hawke-Keating governments.
"If Bill Hayden left no other legacy than as a key architect of universal healthcare, he would still stand for all time as a legend of our labour movement and a great contributor to our nation," Mr Albanese said in a statement on Saturday.
"In a time of forceful personalities, Bill Hayden was notable for his humility.
"Yet there was nothing modest about his ambition for Labor or Australia. This was the quiet strength of character he brought to the cause of progress."
History should record that there could have been no Medicare without Mr Hayden championing and building Medibank, Mr Albanese said.
As social security minister after Labor came to power in 1972, Mr Hayden was the architect of Medibank, the precursor to Medicare.
Bill Hayden was a humble man but there was nothing modest about his ambition for Labor or Australia. — Anthony Albanese (@AlboMP) He brought a quiet strength to the cause of progress and through his lifetime of service, he changed our party and our country for the better. May he rest in peace. pic.twitter.com/rBgJhqSM6POctober 21, 2023
Former prime minister Paul Keating described Mr Hayden as "a great servant of Australia".
"Political circumstances denied Bill Hayden the prime ministership but the Hawke government in which he served as foreign minister was set up and shaped by him as leader of the parliamentary Labor Party," Mr Keating said.
"And the economic personnel he put in place were the building blocks the Hawke government relied upon to shift the country's policy to the economic rationalism which has since made Australia so flexible and so wealthy."
Born in 1933, Mr Hayden grew up in Queensland where he worked in the public service and police force before winning the federal seat of Oxley in 1961, which he held until 1988 before serving as governor-general.
Opposition Leader Peter Dutton said Mr Hayden, a fellow Queenslander and former police officer, put his party and the nation before personal ambition.
"For the man who described himself as 'a product of the Great Depression', Bill Hayden achieved great things in public life, leaving Australia that much greater thanks to his service," Mr Dutton said.
Federal Treasurer Jim Chalmers said in a statement that Bill Hayden was a "selfless servant of the Australian people, and our Party".
A state funeral will be held for Bill Hayden, who served as Australia's 21st governor-general.
Foreign Minister Penny Wong hailed Mr Hayden as a champion of lasting progressive reform.
"As Foreign Minister in the Hawke government, Bill drove closer ties between Australia and Asia and the Pacific region and we continue to deliver on that legacy today," Senator Wong wrote on X.
Deputy Prime Minister Richard Marles described Mr Hayden as "a man of enormous stature" who stands among the giants of the labour movement.
"Be it as the architect of universal healthcare or the nation's first single mother's pension, Bill sought to make this country a better and fairer place for all Australians. He understood the importance of our region and Australia's place in it," he said.
A state funeral will be held for Mr Hayden, who is survived by his wife Dallas and three children.
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