Mr McCain's office said he died on Saturday following his battle with brain cancer.
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".
Tributes have poured in from across the world,
Evangelist Franklin Graham said on Twitter: "Our deepest sympathy and prayers for the family of @SenJohnMcCain. This man gave so much for our nation and will be greatly missed."
President Donald Trump, who once criticised Mr McCain for being taken prisoner during the Vietnam War, said his "deepest sympathies and respect" went out to Mr McCain's family.
Mr McCain's wife Cindy said she was heartbroken by the death of an "incredible man".
In a post on Twitter, she said: "My heart is broken. I am so lucky to have lived the adventure of loving this incredible man for 38 years. He passed the way he lived, on his own terms, surrounded by the people he loved, in the the place he loved best."
John McCain has been described as a man with a quiet faith.
In an interview with megachurch pastor Rick Warren he was asked what it meant to be a Christian. He said: "It means I'm saved and forgiven."
McCain also revealed in his memoirs how prayer sustained him while he was a prisoner of war.
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