The `My Heart Will Go On` singer - who gave birth to the boys via Caesarean section last Saturday (23.10.10) - and her husband Rene Angelil have named the boys after record producer Eddy Marnay and human rights campaigner and former South African President Nelson Mandela, who the star met two years ago.
Celine`s representative told People: "Eddy is a major influence in both Celine and Rene`s lives.
"Rene said that in just the few minutes they were able to spend with Nelson Mandela they were impressed by the human being he is.
"Celine and Rene want their children to be inspired by their names, because they were so inspired by these men."
Meanwhile, the twins - who were conceived after six in vitro fertilisation (IVF) attempts - were released from hospital on 28.10.10 after requiring medical attention due to being born premature.
Dr. Ronald Ackerman, Celine`s obstetrician and gynaecologist, praised the new parents - who also have a nine-year-old son, Rene-Charles - for being "caring and kind".
He told US TV show `Access Hollywood`: "It should be known worldwide that this team of doctors agrees that Celine and Rene are clearly two of the most caring and kind individuals that they have ever cared for."