The frontman and his 41-year-old wife Lisa had been trying for a baby for 15 years, but after d'Abo had an earlier vasectomy reversed, he said: "Suddenly we got lucky."
Twins Ella and Louis are the couple's first children together but d'Abo has three children from two previous marriages.
He said: "We got the shock of our lives when we were told it was twins. We were completely bowled over."
But he claimed he is not worried about becoming a dad again at his age, saying: "We're fit and active and healthy, and in those circumstances your age is just a number."