A statement released by St Mary's Medical Center in West Palm Beach, Florida said the first twin weighed five pounds and 10 ounces (2.55 kg).
His brother, born one minute afterwards, weighed six ounces less (2.38 kg). Dion has been trying to have more children for some time and has spoken publicly about her experiences with in-vitro fertilisation.
Last year the Grammy-winning artist confirmed she was pregnant, only to subsequently suffer a miscarriage. In other baby news, US actor Matt Damon and his wife Luciana have announced the birth of their third daughter together.
The couple are said to be "great" after welcoming Stella Zavala Damon, who was born on Wednesday in New York.
BBC