On the programme and in his memoirs, to be published in October, Fry will explain how close he came to committing suicide after he fled the play Cell Mates two years ago, because of depression.
He says it was only a vision of his parents that prevented him from going through with it.
He tells the psychiatrist Dr Anthony Clare: "I had my hand on the key and a duvet cover around the car door so the exhaust fumes would be kept in. I was deeply, deeply unhappy and lonely."
Fry, who later this year will appear as Oscar Wilde in the film Wilde Life, which is already drawing rave reviews at previews, explains how he felt he had "no right" to be unhappy, particularly as people kept telling him how successful he was.