The Midnight Oil founding member died aged 70, surrounded by loved ones after fighting pancreatic cancer for almost three years.
The Australian band's frontman Peter Garrett led sombre tributes for Hirst, who co-wrote hits such as Beds Are Burning, The Dead Heart, Blue Sky Mine and Power and the Passion.
"For now there are no words but there will always be songs. Love Always from Jim, Martin & Pete," Garrett wrote on social media.
Fellow Australian rockers Cold Chisel, who marked the 15-year anniversary of original drummer Steve Prestwich's death on Saturday, extended their condolences to Hirst's family and bandmates.
In a personal post, Cold Chisel frontman and solo artist Jimmy Barnes hailed Hirst's "massive impact" on Australian culture and dubbed him "the engine driving one of the greatest live bands of all time".
"You are irreplaceable, one of a kind, and myself, my family, and all the rest of this great country will miss you so much," he said.
Prime Minister Anthony Albanese, who was spotted at Midnight Oil's final farewell gig in Sydney in 2022, said Hirst was the "beating heart" of the band.
"For Australians - and for so many fans across the world - Rob built a mighty jukebox that we will always carry in our hearts," he wrote.
"He was a genius. A great Australian. A legend."
Hoodoo Gurus, contemporaries of Australia's 1980s and 90s rock music scene, said the world had lost a great musician.
"You left this world a far better place than the way you found it," the band said.
Hirst went to the same school as former Hoodoo Gurus drummer Mark Kingsmill but formed a close relationship with bassist Rick Grossman.
The band shared an excerpt of a short history Grossman wrote about their friendship during Hirst's final illness.
"When I was a kid around 10 years old I used to fantasise about being in a different family and having brothers. I have a terrific sister and have had wonderful parents but I wanted a brother. And I have had one for 50 years," it read.
Brisbane band Powderfinger described Hirst as an "explosive drumming machine", with Midnight Oil a "huge inspiration" in their formative years.
"It was his mind-bending, perfectly formed, ode-to-Australia, drum solo we rooted for and air drummed to in Power and the Passion," it said.
"It was his songwriting and Keith-Moon-like beat that blew our tiny teenage minds with the in-your-face Species Deceases EP ... Rob and Midnight Oil changed the way we think and how we relate to this land and its first people."
The Bernard Fanning-led outfit supported Midnight Oil at the Woodford folk festival in 1996 and Wave Aid in 2005, and Hirst invited members to have dinner with his family before the rockers broke up in 2010.
"He was wise, welcoming and full of fantastic stories. We laughed and drank into the night, one that we will never forget," Powderfinger said.
"So thank you Rob Hirst. You are an unparalleled performer, musician, commentator, wordsmith and friend. We love you."
Silverchair drummer Ben Gillies also paid tribute to Hirst as an "absolute powerhouse on the tubs", while Troy Cassar-Daley lamented "a big star is missing from our musical sky tonight".
"See you at the next big gig on the other side brother xxx," the Australian country music legend said.
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