Both mother and baby are said to be fine.
This is Kareena's first child with husband Saif Ali Khan, and has been named Taimur Ali Khan Pataudi.
Saif has two children, Sara and Ibrahim, from his first marriage to Amrita Singh.
Kareena's BFF Karan Johar confirmed on Twitter: 'My Bebo had a baby boy!!!!!!! Am so so happy!!!!!!! #TaimurAliKhan'
Saif and Kareena issued an official statement on the birth of their son: 'We are very pleased to share with you all the wonderful news about the birth of our son: Taimur Ali Khan Pataudi, on the 20th of December 2016. We would like to thank the media for the understanding and support they have given us over the last nine months, and of course especially our fans and well wishers for their continued affection. Merry Christmas and a happy new year to you all.'
"The family is delighted. Taimur Ali Khan Pataudi is a beautiful baby boy and both mother and son are doing very well!" Saif's sister Soha Ali Khan told PTI.
Their friends from the industry posted their wishes:
Manish Malhotra: '#congratulations my dearest #kareenakapoorkhan and #saifalikhan #BabyBoy #Taimur Ali Khan Pataudi #Joy #happiness'
Sophie Choudry: 'Woohoooooo ... this is such amazing news!!! #TaimurAliKhan May God bless the little bundle of joy with health, happiness & a bright future'
Tusshar Kapoor: My heartiest congratulations to a favorite costar and my 1st heroine!Following up to a stellar career, now, may this day be the start to an even more glorious life with God's blessing in hand! Cheers to Saif and her both and peace and everlasting joy to the little prince!
Kajal Aggarwal: 'Hearty wishes to the adorable couple #KareenaKapoor and #SaifAliKhan on the arrival of your lil bundle of joy! #TaimurAliKhan.'
Sonam Kapoor: 'Congratulations my darling Bebo and Saif! #taimuralikhanpataudi is going to be the apple of everyone's eye... #mininawab.'
Here's congratulating the new parents!
Kareena's most STYLISH pregnant look? VOTE!
'Kareena and Saif are a solid couple'
PIX: Kareena-Saif party with Amitabh Bachchan, Sridevi
'Kareena is enjoying every moment of her pregnancy'
PIX: Inside Kareena Kapoor's birthday bash!