"I have another brother, whom I love and adore, who I didn't know I had," he told BBC Radio 4's Desert Island Discs.
The singer said he found out about his half-brother in 2000, adding that he is "at peace" with it.
The 62-year-old told host Lauren Laverne that his mother Iris, who died in 1974, did not know her husband had a child with another woman.
"It's a very close family," Bono said, "and I could tell my father had a deep friendship with this gorgeous woman, who's part of the family, and then they had a child. And this was all kept secret."