Aishwarya gave birth to her first child Wednesday morning at Mumbai's Seven Hills Hospital.
"It's a momentous occasion for the family and we are overwhelmed with all the love we have received. From all our fans, the media and the industry. Both Aishwarya and the baby are doing great and we can't wait to have them home," Abhishek said in a statement.
"I would specially like to thank the media for being so supportive, kind and respectful at such an important juncture in our lives," he said.
"It means the world to us. This is a very overwhelming and exciting phase we enter into and hope to have your continued love and support," he added.
Meanwhile, the new father is seeking some parenting tips from his parents Amitabh and Jaya.
"How do women/mothers do it? I'm walking around like a zombie and the Mrs. is like a super trooper with a bit of bionic woman thrown in," the 35-year-old posted on micro-blogging site Twitter.
"Just as I step into fatherhood and parenthood, I've never seen myself rely and depend on my parents more. Guess that happens with every new (sic)," he further posted.
The actor has nicknamed the little girl 'Beti B' and says he spends his whole day noticing the little actions of the child.
"And till we find a name for the little lady a dear friend Shahana Goswami gave me a great one. We have Sr B and Jr B already so... Beti B!...Much like my father SrBachchan I too spent the day observing every little thing about the little one," he posted.
While Abhishek is enjoying his fatherhood, megastar Amitabh Bachchan is in seventh heaven after becoming a grandfather the third time over and he is looking forward to start the process of bringing up the child.
"...Soon we shall be home and then shall start the process of bringing up. Of teaching and bearing and learning. Of etiquette and manners, of religious indoctrination, of schooling and further monitoring...," Amitabh wrote on his blog bigb.bigadda.com.
"A day spent with the new born, observing each movement, breath and presence .. recording it for posterity and for us in our old age," he posted on micro-blogging site Twitter.