Benaud, one of Australia's most influential cricketers and television personalities, died peacefully overnight in his sleep, his family said.
He had been fighting skin cancer and suffered serious injury in a car accident in late 2013.
"A sad day for Australia," tweeted Prime Minister Tony Abbott, who offered a state funeral to Benaud's family.
Flags flew at half-mast, including over the Sydney Harbour Bridge.
The gates were thrown open at the Sydney Cricket Ground where Benaud played and mourners laid flowers around his giant bronze statue.
"We have lost a cricketing champion and Australian icon. What an innings. RIP Richie Benaud," Abbott said.
Benaud last captained Australia against South Africa in the 1963-64 series and went on to become a legend as one of cricket's best known characters and broadcasters.
A pioneer of entertaining, attacking cricket, the veteran of 63 Test matches was the first player to score 2,000 Test runs and take 200 Test wickets.
Australia never lost a series under the leg-spinning all-rounder's captaincy, which ran for 28 games from 1958.
A flamboyant player, Benaud moved into commentary, first with the BBC in England, where he was as well known as in Australia for his dry wit and distinctive style.
"My mantra is: put your brain into gear and if you can add to what's on the screen then do it, otherwise shut up," Benaud said, looking back at his success.
"The key thing was to learn the value of economy with words and to never insult the viewer by telling them what they can already see."
He could also turn a vivid phrase and was inspired by an Ian Botham six during the 1981 Ashes Test at Headingley, part of one of the greatest series ever.
"Don't bother looking for that, let alone chasing it," Benaud commentated. "It's gone straight into the confectionery stall and out again."
He also played a key role in the formation of Kerry Packer's World Series Cricket that revolutionised the professional game in the 1970s, and anchored the billionaire's Channel Nine cricket coverage for decades.
Tributes poured in from around the nation for Benaud, who was born in Penrith, in western Sydney, in 1930.
"My vintage, we grew up with that voice," said current Australian captain Michael Clarke.
"He was a great player and a great captain. A wonderful leader of men and he continued that off the field," Clarke said.
"He loved winning. He helped the Australian team have the attitude where they wanted to win. He played the game the right way."
Benaud took 248 Test wickets at an average of 27.03 and had a highest score of 122 in a remarkable career that saw him take five wickets 16 times.
Indian batting great Sachin Tendulkar called his passing a "great loss to the world of cricket".
Tendulkar said on Twitter Benaud brought "great insights on the game" and that he had fond memories of talking with him and his fellow Australian bowler Shane Warne about the art of leg spin.
Warne left an emotional tribute on Instagram praising Benaud as a hero and "the godfather of cricket".
Another former Australia captain, Steve Waugh, said Benaud was "irreplaceable."
"He was unique as he covered all facets of the game, as a player, a commentator, an administrator and a writer. His legacy to the game will always live on."
International Cricket Council chief executive David Richardson saluted the "stellar" lifetime of one cricket's "most beloved sons".
"Richie was a true legend, charismatic but always the perfect sportsman and gentleman," he said.
Ex-England cricketer Jonathan Agnew, who like Benaud in years past worked on BBC's "Test Match Special", described him as a "true one-off".
"He was quite simply peerless. Nobody else had his authority, popularity and skill.
"He had this unique style – the choice of words, how he delivered them, the way he looked – and it all came together to make him one of the most recognisable people on television."
enaud's popularity and catchphrase "marvellous" propelled him into advertising and he was the mainstay in Australian television commentary before announcing in November 2014 that he had skin cancer.
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