The Most Reverend Justin Welby, 60, had decided to take a DNA test after being approached by 'The Daily Telegraph' with research that indicated he may be the son of Sir Anthony Montague Browne, the last private secretary of Churchill.
The test showed a 99.9779 per cent probability they were father and son. Until the test last month, Welby had believed his father was whisky salesman Gavin Welby, who died in 1977.
His mother, Lady Jane Williams of Elvel, has confirmed she had a "liaison" with Sir Anthony just before she wed in 1955.
Lady Williams had also worked as secretary to Churchill during his final years as prime minister.
In a statement, Welby said: "To find that one's father is other than imagined is not unusual. This revelation has, of course, been a surprise, but in my life and in our marriage Caroline and I have had far worse.
"I know that I find who I am in Jesus Christ, not in genetics, and my identity in him never changes. Even more importantly my role as Archbishop makes me constantly aware of the real and genuine pain and suffering of many around the world, which should be the main focus of our prayers."
The newspaper had spoken to Lady Montague Browne, Sir Anthony's widow, who said she had been aware her husband may have had another child.
Welby said his mother Jane Williams and Gavin Welby were both alcoholics, adding his mother had been in recovery since 1968, and had not touched alcohol for almost 50 years.
Gavin Welby, a whisky salesman, died "as a result of the alcohol and smoking" when Welby was 21.
"As a result of my parents' addictions my early life was messy, although I had the blessing and gift of a wonderful education, and was cared for deeply by my grandmother, my mother once she was in recovery, and my father (Gavin Welby) as far as he was able," Welby said.
Lady Williams said the news had come as an "almost unbelievable shock" as her son was born almost nine months to the day after she married Gavin Welby in the US in 1955.
She said her then-husband was putting pressure on her to leave her job as personal secretary to the Prime Minister and run away with him at the age of 25.
In a statement she said: "One feature of this pressure is that I was already drinking heavily at times.
"Although my recollection of events is patchy, I now recognise that during the days leading up to my very sudden marriage, and fuelled by a large amount of alcohol on both sides, I went to bed with Anthony Montague Browne.
"It appears that the precautions taken at the time didn't work and my wonderful son was conceived as a result of this liaison."
IMAGE: The Archbishop of Canterbury Justin Welby arrives at the Cathedral Church of Holy Trinity in Burundi's capital Bujumbura. Photograph: Evrard Ngendakumana/ Reuters