The 'My Heart Will Go On' singer is believed to have delivered the two babies via Caesarean section on Saturday (23.10.10) at St Mary's Medical Centre, in West Palm Beach, Florida, at 11.11am and 11.12am.
The fraternal twins ' which means they are non-identical siblings ' weighed in at 5lbs 4oz and 5lbs 10oz.
Although they are both healthy, the babies will spend the next few days in incubators because they were born premature. The due date had been in November.
A representative for the 42-year-old pop star ' who also has a nine-year-old son Rene-Charles with her husband Rene Angelil - said: 'Celine, Rene and their son Rene-Charles are thrilled . Celine is resting now and they plan to discuss what to name the boys when she wakes up
'Rene-Charles has been to the hospital to visit his brothers and is just so excited they are here.'
The twins were conceived via in-vitro fertilisation (IVF) just as Celine and 68-year-old Rene's first child Rene-Charles was.
The Canadian singer previously revealed she underwent six gruelling courses of IVF to get pregnant again and admitted the process was 'mentally exhausting'.
She said: "I feel like I've been pregnant for over a year. I never gave up. But I can tell you that it was physically and mentally exhausting."