The Archbishop of Canterbury said that the revelation that his biological father is Sir Winston Churchill's last private secretary is a "complete surprise".
The Most Rev Justin Welby, who believed his father was Gavin Welby, said he found out through a DNA test that his biological father is the late Sir Anthony Montague Browne.
His mother, Lady Williams of Elvel, 86, described the revelation as "an almost unbelievable shock", but added she recalls going to bed with Sir Anthony "fuelled by a large amount of alcohol on both sides".
In a statement, she added: "It appears that the precautions taken at the time didn't work and my wonderful son was conceived as a result of this liaison."
Welby said the discovery was made recently, and in a statement of his own, he said: "In the last month I have discovered that my biological father is not Gavin Welby but, in fact, the late Sir Anthony Montague Browne.
"This comes as a complete surprise."
He added: "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."
Lady Williams said: "Although, as has already been made public, Gavin Welby and I had a short and, sadly, dysfunctional marriage, neither of us ever doubted that we were the parents of our son Justin, who was born almost nine months to the day after our marriage in America on April 4 1955.
"I still recall our joy at his arrival. So this DNA evidence with which I have now been presented proving that Gavin was not Justin's biological father, so many years after Gavin's death, has come as an almost unbelievable shock."
Welby said his mother Jane Williams and Gavin Welby were both alcoholics, adding that his mother has been in recovery since 1968, and has not touched alcohol for more than 48 years.
"I am enormously proud of her," he said.
The Daily Telegraph reports that Welby decided to take paternity test after the newspaper approached him.
Gavin Welby died "as a result of the alcohol and smoking" in 1977, when the Archbishop was 21.
Lady Williams, who split from Gavin Welby in 1958, married Baron Williams of Elvel in 1975.
She has described her ex-husband Gavin Welby as "a very strong, possessive character", adding: "At the end of March 1955 he was bullying me to leave my job as personal secretary to the Prime Minister and run away with him and marry him in the United States where his divorce was being finalised.
"At the age of 25, as I was, the pressure became too great and in the end I found myself unable to resist.
"One feature of this pressure is that I was already drinking heavily at times.
"Although I could then ensure that this did not affect my work, it was later to develop into serious alcoholism during the 1960s which only came to an end when I entered rehab in 1968. I have not drunk alcohol since.
"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."
She said that after leaving her job and getting married, she did not see Sir Anthony again for a long time.
"After Gavin and I broke up in 1958 Anthony and I met occasionally but although he may have asked how Justin was, there was nothing that gave me any hint that he might have thought he was Justin's father," she said
In his statement Welby said: "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."
He said his own experience is "typical of many people", adding: "To find that one's father is other than imagined is not unusual.
"To be the child of families with great difficulties in relationships, with substance abuse or other matters, is far too normal."
Welby said: "Although there are elements of sadness, and even tragedy in my father's (Gavin Welby's) case, this is a story of redemption and hope from a place of tumultuous difficulty and near despair in several lives."