It concluded: “We kindly ask that their wishes are respected as they come to terms with this devastating loss and take the time they need to grieve.
“We thank everyone for their prayers and messages of love and continued support.
“With love, the Anderson family and Rose Tattoo band. Stay young, grow strong.”
News of Anderson’s death follows the band announcing they would be ending their European tour early after he suffered a cardiac arrest.
They had been scheduled to return to Australian stages this month, as well as being signed up to join Suzi Quatro on her Red Hot Summer Tour, which kicks off in November.
Rose Tattoo are most famous for tracks including Bad Boy for Love and We Can’t Be Beaten, and released their most recent album Outlaws in 2020.
They were also inducted into Australia’s Aria Hall of Fame in 2006.
Previously speaking to Sheldon Ang about celebrating 50 years of Rose Tattoo, Anderson mused: “There’s a voice inside you that says you need the freedom of the road … even at 77.
“I still say that on stage every night … it’s f***ing great being a singer in this band … regrets, I have but a few, but too few to mention.
“It has been a fabulous ride. It still is.”