In a statement on Wednesday, Farham's wife Jill and sons Rob and James said the singer was in a stable condition.
"John has been through an eleven and a-half hour surgery in Melbourne yesterday and is now in a stable condition in ICU," Jill wrote.
"The cancer tumour was located in his mouth and it has been successfully removed.
"There is still a long road of recovery and healing ahead of us, but we know John is up for that task."
The family paid tribute to hospital staff and thanked the public for their well wishes.
"We are in awe of the incredible teams of health care professionals who have guided us through this very challenging time with such compassion," they said.
"To all the surgeons, doctors, nurses and consultants - thank you one and all so very much."
The singer's operation began at 8am on Tuesday in a Melbourne hospital and was successfully completed at 7.30pm that night.
Before his surgery, Farnham, 73, said a cancer diagnosis was something many people faced each day "and countless others have walked this path before me".
"The one thing I know for sure is that we have the very best specialist health care professionals in Victoria and we can all be grateful for that. I know I am," he said.
It comes three years after Farnham suffered a health scare and was hospitalised with a severe kidney infection.
Farnham sang his way into Australian hearts as a fresh-faced teenager in the 1960s, but had faded into near-obscurity before his 1986 album Whispering Jack shot him back to the top some 20 years later.
The album produced one of the nation's best-known anthems, You're the Voice, and propelled Farnham to hero status.
He followed up Whispering Jack with his chart-topping albums Age of Reason (1988) and Chain Reaction (1990).
Farnham was born in 1949 in Dagenham, England. He emigrated to Australia aged 10 with his family, who settled in Melbourne.
News of Farnham's cancer diagnosis prompted an outpouring of well wishes across the country.
Prime Minister Anthony Albanese on Tuesday said all Australian's loved him.
"John Farnham has been and continues to be a great Australian. He has not only provided entertainment for Australians over many decades, he also has been a contributor to the nation," he said.
Victorian Premier Daniel Andrews said he was a wonderful person.
"I wish him and his family well in what is surely a very difficult time," Mr Andrews said.
