The singer's representative, Cindi Berger, confirmed the births at 12.07pm (5.07pm BST) on Saturday at a hospital in Los Angeles.
Ms Berger said the baby girl was born first, weighing 5lbs 3oz and was 18ins tall. Her brother was next, at 5lbs 6oz and was 19ins.
Ms Berger said the couple had not named the children yet. Nick drove Mariah to the hospital in their Rolls-Royce Phantom. Ms Berger said the 41-year-old, who had gone through false labour, was calm, thinking that it was another false alarm.
Meanwhile, Nick, 30, was so nervous he went to the wrong department at the hospital and was guided to the maternity ward by a nurse.
"It was like right out of an I Love Lucy skit," said Ms Berger, referring to the 1950s TV comedy.
Ms Berger said they were listening to Mariah's We Belong Together after the children were born.
The couple are expected to renew their wedding vows. The pair got married in 2007 after a whirlwind romance. They were the subject of endless baby rumours, and the couple actually were expecting shortly after their marriage, but Mariah had a miscarriage. They did not reveal the miscarriage until she announced her pregnancy last autumn.
The couple plan to live a bi-coastal life, and have luxurious nurseries in both New York and Los
