Shah Rukh, 47, made the news official about his surrogate baby via a statement.
"Amidst all the noise that has been going around, the sweetest is the one made by our newborn baby, AbRam. He was born prematurely by several months, but has finally come home," said Shah Rukh.
"Gauri and our whole family have been dealing with his health issues for a long time now," he added.
Explaining his longstanding silence on the matter, he said: "As a family, our silence on this subject has been because of the personal nature of emotional strife that we have been going through due to his health."
The superstar, also called the 'baadshah' of Bollywood, also put the record straight that "there was no sex determination for our child".
"The baby was born much before the speculations of 'sex determination' and other 'issues' pertaining to the same were being raised in the media by some organisations. Suffice to say his coming home puts to rest completely false and at times insensitive claims of sex determination and alleged illegalities," he added.
On his part, the actor-producer has also apologised to "all those other doctors and hospitals who had to face unwanted scrutiny and questioning by some parties", and he has thanked the doctor concerned, Jatin Shah, for his expertise and contribution to make the surrogacy successful.
"We also wish to thank all the other doctors, nurses and medical staff who have made his life possible," added Shah Rukh, who also said the entire surrogacy process is bound by "strict confidentiality".
He has appealed to all "to allow us to cherish this private moment as a family".
Shah Rukh, who began his tryst with showbiz through the small screen in 1988, married Gauri in 1991. They have two children together - son Aryan,16, and daughter Suhana, 13.