"Both Aishwarya and the baby are doing great and taking some much needed rest," tweeted Abhishek Bachchan on his twitter account. He also thanked his fans by stating, "Thank you all for your prayers and good wishes."
Aishwarya Rai delivered a baby girl this morning, and it was Abhishek who broke the news on twitter, saying: "It's a girl."
Amitabh later tweeted that he was a 'Dada to the cutest baby girl.'
Since then, the family had not tweeted anything, even though the film industry wished them warmly on twitter.
Six hours later, Abhishek updated the world about his family.
He added: "And I'm trying my level best to get rid of this caffeine high and get some sleep too. Don't think it'll work. TOO EXCITED!!!!"
The baby has been born in Seven Hills hospital, in Marol, northwest Mumbai.
Ash, who was admitted on Monday night, was accompanied by Abhishek, Amitabh and Jaya Bachchan, Shweta Nanda and her son Agastya, Vrinda and Krishnaraj and Ash's brother Aditya.
Amar Singh, Sonali Bendre and Goldie Behl were among the first to visit Ash after the baby was born.
Photograph: REUTERS/Tyrone Siu