Quax had been battling cancer.
In January, he told the New Zealand Herald: "I'm not dying from cancer, I'm living with cancer."
A former world record holder, Quax won silver in the 5000m at the 1976 Montreal Games.
He won silver in the 1500m at the 1970 British Commonwealth Games. In 1977 he had set a world record for the 5000m.
Olympic gold medallist Sir John Walker was close with Quax not just on the track, but off it as well; with both heading into local politics as councillors at the then Manukau City Council and then Auckland Council in their later years.
Walker paid tribute to a man he called a good friend, colleague and running mate.
"Dick was one of the fiercest and hardest working competitors on and off the track,'' he wrote online.
"He helped me a lot as a young athlete and I will always be grateful for our time shared during and after our running careers and above all else, getting to know a great man and friend."
Auckland mayor Phil Goff offered condolences to his colleague's family on behalf of the Auckland Council as well as the people of the city.
"Our thoughts and prayers go out to his wife Roxanne and his children.
"[Dick] was a passionate contributor in council debates, advocating strongly on behalf of his constituents. We remember him also as one of New Zealand's finest athletes, representing us at the Olympics and international events.
"Dick battled his illness with courage and continued to work as long as he could on behalf of his community."
In 2001 he was elected to the Manukau City Council and was re-elected in 2004.
In October 2007 he contested the Manukau mayoralty, but lost to Len Brown.
Another running great, Rod Dixon, said Quax died this morning.
"Right now this is the most emotional time, my great friend and competitor passed away peacefully in New Zealand this morning," he said on Facebook.
"To his family my condolences and love at this most difficult time.
"Peaceful journey my great friend."
Quax, with Walker and Rod Dixon, was one of New Zealand's leading distance runners of the 1970s.
In the 1976 Olympic 5000m final, which also included Dixon, he was beaten by a stride in a dramatic last lap by Lasse Viren, of Finland.
Quax missed out at the first Super City elections in 2010, but was elected in a byelection after Jami-Lee Ross resigned to become an MP.
Botany MP Ross, whose political career also began at the Manukau City Council, told the Herald they had had a close relationship that spanned about 14 years.
"Dick was a great guy. He obviously had a huge reputation as an Olympic hero for the country and did an amazing job in athletics.
"But he was also a staunch advocate and a vocal supporter of everything for his community in Howick and Pakuranga. He was always someone who was not afraid to take on big fights for the community and someone who had passion for the locals.''
Ross acknowledged many locals knew him for his work in politics, but his friend was very much a proud dad and family man.
"We spent a lot of times in cars going to meetings or putting up election signs or campaigning together.
"And the conversations I remember the most about Dick was [when] he discussed his boys, Jacob and Theo, as they grew up. He was such a proud dad of everything they did academically and sporting-wise.
"People would think that councillors and politicians will always talk about politics. But so often, Dick would talk about his boys and how well they were doing and how proud he was of them growing up. It was a really cool part of Dick that I don't think the public saw as much as I think they should've.
"He was so focused on his boys and his wife Roxanne."
Auckland councillor Sharon Stewart and Pakuranga MP Simeon Brown released a joint statement expressing their sadness over their colleague's passing.
"My thoughts and condolences are with Dick's family; his wife Roxanne, and his three children, Tania, Jacob, and Theo," Stewart said.
"Through hundreds of calls and text messages since the news broke, I know the people of Howick grieve with them at this difficult time and join me in thanking Dick for his service to our community over so many years.
"I feel particularly lucky that I had the chance to serve alongside him in Auckland Council and can personally attest to his unwavering commitment to the job, even as he battled cancer.
"On bed rest from his home in Sunnyhills, he was instrumental in the repairs to the Rotary Walkway being completed ahead of schedule earlier this year and was determined to ensure the people of Howick were represented even through his illness."
He stood for Parliament for Act in 1999 and 2002. In 2007 he was beaten by Len Brown for the Manukau mayoralty. His family came to New Zealand from the Netherlands in 1954.
