The baby boy was born premature and was treated at three different hospitals.
His baby was born four weeks premature at Masrani Hospital in Andheri on May 27, said doctors who treated him.
He weighed just 1.5 kg at birth and developed complications that doctors at Masrani found difficult to treat.
Khan, after consultations, shifted his son to Nanavati hospital. His confidence in Nanavati is well known as he has been undertaking physiotherapy sessions at the hospital. However, doctors at Nanavati could not do much for his baby, whose condition had become more critical by then.
Khan was then advised to take the baby to Breach Candy hospital.
The neo natal care in Breach Candy is much better and specialised than Nanavati, hence Shah Rukh moved the baby to Breach Candy hospital. The condition of the baby got critical and the family was worried by then.
The baby boy since then has made a quick recovery. After spending three weeks in incubator in the neo natal care, the baby now is with his parents at Khan's home, 'Mannat'.
According to some reports, the actor's sister-in-law Namita Chibber could have given birth to the baby. However, there is no confirmation on the same.
Shah Rukh Khan also got embroiled into a controversy over whether the actor and his wife had undergone an illegal prenatal sex test.
"Andheri hospital has informed the BMC health authorities that a boy was born on May 27, 2013," said Vijay Khabale Patil, a spokesman for the Brihanmumbai Municipal Corporation (BMC).
"The father's name was Shah Rukh Khan and the mother was Gauri Khan," he told AFP.
The Khans, already parents to a teenage son and daughter, have made no announcements on the matter but it is standard procedure for hospitals to give details of births in the city to the BMC.
Back in 2011, fellow Bollywood megastar Aamir Khan and his wife also had a baby boy using a surrogate mother.
The news that the birth was as far back as May means the child was born before rumours surfaced in the media that the Khans were expecting a boy, raising suspicions of an illegal sex test on the foetus.
India bans sex tests because of a preference for sons in the country. Female foeticide has led to a major population imbalance between the sexes.
Khan, star of "Dilwale Dulhania Le Jayenge" and "My Name Is Khan", topped the first Forbes India Celebrity 100 list earlier this year with annual estimated earnings of $37.7 million.