Neeson is survived by his partner Annie Souter and four children.
Auckland music promoter Brent Eccles, who was the drummer in The Angels between 1981 and 2000 and managed the band during the 90s last saw Neeson two months ago.
He remembered his bandmate as an intelligent man who combined an in-your-face performance style and instilled his "big thinking" into his lyrics.
"He'll be greatly missed. I don't think I have known anyone quite like him. He was a mad Irishman."
The singer was born in Belfast, Ireland in 1947 and migrated to Adelaide, Australia with his family when he was 13-years old.
He was studying to become a teacher when he was drafted into the Australian army in the late 1960s. But he avoided the Vietnam War when the army became aware of his education training. He was sent to Papua New Guinea to teach the Pacific Island Regiment.
Neeson later took advantage of a returned soldiers' scheme to study filmmaking in Adelaide. He met musicians in Adelaide and formed the Moonshine Jug and String Band, which morphed into the Keystone Angels and then the Angels.
The Angels became Australia's highest-paid band by the late 1970s and were frequent visitors across the Tasman.
The band continued with a string of hits into the 1990s, with Neeson as singer/songwriter and high energy frontman
Guitarist John Brewster said Neeson used an oxygen tank off stage in the early days during some particularly crowded gigs in small venues.
"Doc's singing all this stuff and he's belting it out, and those songs are fairly frenetic, so Doc would be literally running out of air so we had this oxygen tank."
The Angels' first single, Am I Ever Going to See Your Face Again, released in 1976, became a youth anthem. Audiences around Australia reply with same expletive-laden response to the song's chorus decades later.
Neeson said he heard what he described as "the response" or "the chant" from audiences in London and the Middle East, as well as around Australia.
"In a way, I'm really delighted to hear that because it's Australian audiences making the song their own," Neeson said in an ABC interview aired in April.
"When the band had first started, we were trying to write songs for Australian audiences and they've made it their own in a way I never would have thought possible," he said.
Neeson suffered a setback in 1999 when, one week before he was due to perform for Australian troops in East Timor, he was injured in a car accident. The singer went ahead with the performance despite being in chronic pain.
Governor-General Peter Cosgrove, then commander of the INTERFET forces in East Timor, later described the singer as "a rascal, but a very good rascal".
On his return to Australia, Neeson continued to struggle with pain and depression after the accident and stopped performing with the Angels.
Soon "divisions in the band" began to emerge, original drummer Graham "Buzz" Bidstrup told the ABC. The Brewster brothers continued to tour with different line-ups. "Unfortunately ... there was a big split in The Angels," Neeson said on the programme.
Bidstrup described the situation as "nasty". "It did get nasty around the time, the way that it started to manifest itself was, you know, if one side couldn't own the name, they were going to stop the other side from using it.
"No one's shy in this band about saying what they like or they hate," Bidstrup said.
Neeson began performing again on-and-off from 2003, in his band Doc Neeson's Angels. In 2012, Neeson had a seizure and was diagnosed with a high grade brain tumour.
Midnight Oil drummer Rob Hirst remembered a benefit night held for Neeson in April 2013.
"It was incredible that Doc, who was clearly not feeling well, rallied himself to show up on the night. That shows the kind of fellow Doc was, he was born to perform," Hirst said.
Three weeks after the "Rock for Doc" concert, Neeson was presented with an Order of Australia by New South Wales Governor Marie Bashir.
Midnight Oil frontman Peter Garrett paid tribute to Neeson as a "big man with a huge heart" as Angels fans flooded social media with condolences on the death of the singer frontman.
"A mighty talent ... You showed us how," Garrett tweeted.
Aussie fans hailed the performer as a true showman and a member of Australian rock royalty. Others fondly remembered listening to the band's string of hits in the late '70s and '80s.
"Most potent memory of young suburban life was watching The Angels blow the roof off Blacktown RSL sometime early 80s," Adrian Michaels tweeted.
Some tweets affectionately remembered Neeson as the voice behind Am I Ever Going To See Your Face Again: "No way, get f***ed, f*** off!"
The Angels' string of hits also included Coming Down (1978), Take A Long Line (1978), After The Rain' (1978), Shadow Boxer (1979), No Secrets (1980), Fashion and Fame (1980), Stand Up (1982), Eat City (1983), Live Lady Live (1984), Nature of the Beast (1986), Don't Waste My Time (1986), We Gotta Get Outta This Place (1987), Finger On The Trigger (1988), Let The Night Roll On (1990), Dogs Are Talking (1990), Back Street Pickup' (1990), Tear Me Apart (1992).
Watch The Angels' Face the Day
Watch The Angels' No Secrets
-AAP/AP/Herald online