Her husband Rene Angelil was at her side during the caesarean section to deliver the babies on Saturday.
The thrilled father even cut their umbilical cords. One twin weighed 5lbs and 10oz. His brother, born one minute afterwards, weighed 5lbs and 40z.
"It's the greatest thing that could happen to us," said the 68-year-old. "I hope to provide to them all of the love that I can for as long as I can."
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In this week's HELLO! in an interview just before giving birth, the 42-year-old singer details her long battle to conceive the boys, who are siblings for the couple's nine-year-old Rene Charles.
Speaking exclusively from her palatial mansion in Florida, the singer described having six gruelling cycles of IVF.
"I am not somebedoy who's going to say: 'It didn't work,' for hours," she said.
"You have to be patient. It's difficult emotionally, but you don't want that to affect you so much that suddenly you forget your husband, your forget yourself, your forget your son".
Luckily, her patience was rewarded in the end. The babies are healthy, but they will spend the next few days in an incubator because they were premature.
Pick up your copy - issue number 1147 - out now, for the full story.