The lecture, which will be broadcast live on BBC Radio 4 and on BBC World Service, will celebrate the life of Cooke who died last year aged 95 after presenting BBC Radio 4's 'Letter from America' for 58 years.
The lecture is a joint initiative between the BBC and friends and colleagues of Cooke, led by Richard Price, the former chairman of Bafta and Fellow of the Royal Television Society.
McCain was once described by Cooke as a "hero with a gift for believable indignation". The title of his lecture is 'An American Patriot Today', in which he will maintain that "to be an American patriot is to support a moral mission at home and abroad".
McCain has had a long career in and out of politics. He was famously shot down while fighting in Vietnam in 1967 and endured five-and-a-half years as a POW in Hanoi.
He went on to be decorated numerous times and was elected to Congress in 1982 for Arizona. He became a Senator for that state in 1986. He was a candidate for the Republican Presidential nomination in 2000.
McCain said that Cooke not only gave America a sense of its relationship with the British, but also a good dose of British culture and history.
"In this lecture, I'll be talking about the unique relationship that exists between the US and the British, and the challenges that lie ahead," McCain said.
BBC Radio 4 has replaced 'Letter from America' with a comment slot, which is set to feature a number of significant commentators. The slot is current being filled by former political heavyweight journalist Brian Walden.
Walden is to be followed by the writer and former Sunday Times editor Sir Harold Evans, who will take over from Walden on July 29 for a 13-week run.
The BBC said it is in talks with a number of other "significant commentators", but added that there would be no return of 'Letter from America'.
The lecture is to be given at the English Speaking Union, Dartmouth House, London, and will be chaired by Nick Clarke, Alistair Cooke's biographer and the presenter of Radio 4's 'The World at One'.
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