"Thank you all for your prayers and good wishes. Both Aishwarya and the baby are doing great and taking some much needed rest," Abhishek posted on micro-blogging site Twitter.
Aishwarya gave birth to her first child Wednesday morning at a private hospital in Mumbai.
Congratulatory messages for the parents, and grandparents - Amitabh and Jaya Bachchan, poured in soon after Abhishek announced ""IT'S A GIRL!!!!!! :-)))))" on micro-blogging Twitter. He had recently said he wanted a daughter who looked like Aishwarya.
He is so excited that he is unable to sleep.
"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!!!!" added the proud father, who always wished to have a daughter.
Proud grandfather Amitabh Bachchan too couldn't control his happiness and tweeted: "I AM DADA to the cutest baby girl, A dada ji ... Ecstatic."
Hospital sources said the delivery was normal and came a few minutes before 10 a.m. The Bachchan and Rai families were present for the momentous occasion.
Aishwarya, 38, developed labour pains around 4 a.m. and was taken to the labour room where the delivery took place after nearly six hours.
The actress is on the fifth floor of the luxury private hospital in Andheri east.
The hospital had booked three rooms on the floor -- one for Aishwarya, the other for the Bachchan family and the third for the Rai family. The entire floor was kept out of bounds for all except the two families.
The hospital has been under tight security for the past three days in expectation of the youngest member of the Bachchan family.
Aishwarya was admitted to the hospital Monday night, according to her spokesperson.
The Bachchan family had been waiting for the baby's arrival for a few days and preparing for the child's welcome.
The girl is Amitabh and Jaya Bachchan's third grandchild, after Agastya and Navya Naveli -- children of his daughter Shweta and son-in-law Nikhil Nanda.
Aishwarya tied the knot with Abhishek in April 2007 and rumours about her pregnancy had been doing the rounds ever since.
In June this year, when Amitabh announced her pregnancy through Twitter, it grabbed the headlines.
A 10-point advisory by the Broadcast Editor's Association (BEA) reportedly asked TV channel heads to curtail media coverage regarding the high-profile delivery.
Warm B-town welcome for Abhi-Ash's daugther
The birth of Aishwarya Rai and Abhishek Bachchan's first child, a baby girl Wednesday, brought cheer in tinsel town as celebrities like Anupam Kher, Javed Akhtar, Sonam Kapoor and Bipasha Basu tweeted congratulatory messages to the Bachchan family welcoming the little "angel".
Aishwarya delivered her bundle of joy at a private hospital in Mumbai a few minutes before 10 a.m.
Soon after Abhishek tweeted ""IT'S A GIRL!!!!!! :-)))))", and proud grandfather, megastar Amitabh Bachchan posted "I AM DADA to the cutest baby girl, A dada ji ... Ecstatic" on the micro-blogging site, good wishes started pouring in.
Here are some of the congratulatory messages:
Karan Johar: Congratulations!! Baby B had a baby girl!! @juniorbachchan!!! All the love and happiness...am sure she will be the prettiest girl ever!!!Bipasha Basu: OMG! So excited Baby B is daddy to a li'l Angel! Congrats Ash n @juniorbachchan and to the entire family! Welcome sweet baby girl:)
Javed Akhtar: @SrBachchan. Congratulations Amitabh ji, this has evoked my memory of the day when Shweta was born. Time flies and how swiftly!!
Anupam Kher: CONGRATULATIONS @juniorbachchan and Ash. So so Happy. May the new arrival in the family bring more happiness, joy and peace. Love.:)
Arjun Rampal: Congratulations daddy cool @juniorbachchan and the coolest Dadaji @SrBachchan and the most beautiful mommy Ash and the lovely dadi Jayaji.
Divya Dutta: @SrBachchan heartiest cngratulations sir!
Boman Irani: @SrBachchan Dadaji!!!!!! All of us here are delirious with joy! Bless you all! @juniorbachchan OHHHH MAAAARAAAAA BAAAAAAP!!!!! Overjoyed my darlings!!!!!!
Raveena Tandon: @SrBachchan CONGRATULATIONS my dearest Amitji! Love to ash and Abhishek!! God bless the li'l Angel!
Sonu Sood: Congrats @juniorbachchan...the cutest angel arrives...A BIG HUG BRO:-)
Sonam Kapoor: CONGRATULATIONS @SrBachchan and @juniorbachchan!! I'm so so excited for you! Lots and lots of love and happiness!Celina Jaitley: Very happy for the Bachchan family...They have a little angel fairy amidst them...She is gonna be gorgeous :)
Shreya Ghoshal: Heartiest congratulations to Aishwarya Rai and @juniorbachchan. I am so so excited :)
Tisca Chopra: Congratulations @SrBachchan for yet another challenging role- Dadaji!!
Aftab Shivdasani: Very very happy for my buddy @juniorbachchan on becoming a father to a beautiful baby girl!! God bless :)
Vishal Dadlani: @juniorbachchan Woohoooo!!!! Thrilled!!! Congratulations again, to you and the Memsaab! Love, blessings, best wishes, always!!! @SrBachchan Congratulations, Sir!!! What great news!!! :D Thrilled for all of you! Our very best wishes, as always, and much love!
