Banton, 61, became a nationwide symbol for workers' rights after battling construction giant James Hardie to win a $4 billion compensation package for workers who suffered from asbestos-related diseases.
His family has been offered a state funeral, with Rudd and his wife, Therese, to attend.
In Brisbane this morning, Rudd said, "I would like to honour the life of Bernie Banton."
"I went and saw Bernie at his West Pennant Hills home with his partner, Karen, and her son Dean about four or five weeks ago.
"It struck me then that there was in Bernie the determination to keep fighting and to keep living.
"He was talking about life two to three years down the track and what he could be doing for those who suffered from asbestos-related diseases and mesothelioma in particular."
Rudd said he was shocked by how quickly the disease had taken Banton.
"And I was shocked at the news of his passing this morning."
Rudd said he had spoken to Mrs Banton this morning.
"She's a really strong woman and I honour her, and their son Dean and Bernie's son, Adam - and their other children - for the enormous support that's been extended to Bernie in what has been a terrible period with this insidious disease."
Only last Thursday Banton won a confidential payout as compensation for his terminal mesothelioma, after he was awarded $800,000 compensation for asbestosis in 2000.