The statement went on to say: "Our family is immensely grateful for the support and kindness of all his caregivers over the a year ago, and for the continuing outpouring of concern and affection from John's many friends and associates, and the many thousands of people who are keeping him in their prayers".
"In the year since (his diagnosis), John has surpassed expectations for his survival", the family said Friday.
His family had previously said he had ended medical treatment for the condition, revealing that "the progress of disease and the inexorable advance of age render their verdict".
They said he chose to stop his treatment "with his usual strength of will". She added, "John McCain and I disagreed on many things, and sometimes quite forcefully".
"There is no reason for me to hold a grudge or anger", McCain said.
"We dispirited our base and we let spending get completely out of control".
McCain was finally freed after five and a half years, two of which he spent in solitary confinement.
Former vice-president Joe Biden, who developed a friendship with McCain while they served together in the Senate, said the Arizona lawmaker will "cast a long shadow".
Daughter Meghan McCain described her father as a "great fire who burned bright".
In the book, written in deepening recognition of his own mortality and at a polarized political moment, McCain wrote: "Before I leave, I'd like to see our politics begin to return to the purposes and practices that distinguish our history from the history of other nations". We are fellow Americans, and that's an association that means more to me than any other'. "That is the biggest fallacy in the world - if anything, we're dumber. Even in times of political turmoil such as these, we share that awesome heritage and the responsibility to embrace it".
McCain found Putin's growing influence on the world stage particularly worrisome. Senator McCain led a long struggle to remove "earmarks" or pork-barrel amendments from the American legislative process, annoying Republican and Democrats alike.
In Europe, some condolences also hinted at McCain's role as a vocal critic of the current administration.
A Vietnam POW and a known defense hawk, McCain lost his bid for the White House to Barack Obama in 2008. McCain later said he regretted picking Palin.
Former Presidents Obama and George W Bush are expected to give eulogies.
The six-term senator and 2008 Republican presidential nominee was diagnosed after doctors discovered his tumour during surgery to remove a blood clot from above his left eye last July.
McCain - born on on August 29, 1936 in the Panama Canal - served in the Navy until 1981 and quickly dove into politics.
He attended 20 different schools on his way to graduating from a private boarding school in Virginia in 1954.
McCain broke both arms and one leg after ejecting from the plane. He landed in a lake in the corner of the capital of North Vietnam, he said in recalling the incident. He was severely injured and taken prisoner. On the ground he was beaten and stabbed with a bayonet by North Vietnamese soldiers. He was not released until March of 1973.
He suffered, as the nation suffered, from the morass of Vietnam.
During a 1967 bombing run over Hanoi, McCain's plane was shot down, almost killing him.
He was elected to the U.S. House of Representatives from Arizona in 1982 and to the U.S. Senate in 1986. Chuck Schumer (D-NY) announced that he wants to name the Senate building that housed McCain's suite of offices after the Arizona senator, who served as chairman of the Commerce Committee and the Senate Armed Services Committee.