The charity campaigner died at Cabrini Hospital in Melbourne on Wednesday morning, aged 88.
His family led tributes, saying he will be sorely missed for his energy and good humour.
"Fr Bob was not just a much loved family member but was loved by all Australians for what he stood for," the Maguire family said in a statement.
"He has fought bravely for the underprivileged and homeless all his life. He represented the highest of principles, and he fought to actively live those principles."
Prime Minister Anthony Albanese said the country had "lost a great Australian".
"An irrepressibly cheerful champion for all those battling disadvantage, he dedicated his life to brightening the lives of those most in need," he tweeted.
The self-described larrikin dedicated his life to charitable works and earnt a reputation as a candid commentator who was unafraid to speak his mind or call out church leaders.
The Catholic priest became known for his work with disadvantaged people in his South Melbourne parish before regularly appearing in national media.
He first worked with broadcaster John Safran in 2004 on SBS's John Safran vs God, with the duo going on to host radio programs on ABC's Triple J for a decade.
The pair were often referred to as an odd couple and covered many topics including religion, culture and politics with a side of irony and humour.
"I never thought Bob would ever stop making me laugh, but with the sad news of today, he finally has," Safran posted to social media.
Fr Bob balanced his media commitments and parish duties until he was forced to retire from the Catholic Church.
He was first asked to resign aged 75 under canon law but managed to stay on for another two years even after a public spat with then-Archbishop of Melbourne Denis Hart over finances.
In 2011, he accused Cardinal George Pell of punishing him for being "open to all" and described his exit as a dishonourable discharge.
He performed his last service to a packed crowd of more than 1000 people in 2012.
His final years as parish priest were depicted in the documentary film In Bob We Trust, which includes snippets of his run-ins with church figures.
At 25, he was ordained in Melbourne and was a chaplain for conscripted Australian soldiers heading to Vietnam.
Father Bob was appointed to the parish of Saints Peter and Paul's in South Melbourne in 1973, where he stayed for the next 39 years.
He encouraged people from all walks of life to take part in the community he helped nurture and fiercely advocated on their behalf.
He was appointed a Member of the Order of Australia in 1989 for services to youth homelessness and collected other accolades including Victorian of the Year in 2011 and Victorian Senior of the Year in 2022.
He co-founded national homeless youth organisation Open Family Australia in 1978 and later the Father Bob Maguire Foundation.
In December 2022 he told AAP far greater action was needed on the "national disaster" of homelessness, and in the same interview urged Australians to "brighten up" and focus on what gave them joy.
"You are a child of the universe, you've got a right to be here and all the talents needed not only to survive but to flourish," he said.
The foundation advised Father Bob had stepped down as chairman and board member last week after his health deteriorated.
Foundation board member Frank O'Connor said Fr Bob had communicated his dying wishes to his family over the past year but wasn't aware if they would accept any offer of a state funeral.
"Bob wasn't always one that felt authorities like governments or what have you did the best thing by the people he was worried about," Mr O'Connor said.
"But he'd probably be quite honoured for that sort of thing."