The baby was born in Mumbai's Breach Candy Hospital on Tuesday morning.
In a statement, Kareena and Saif said: "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 9 months, and of course especially our fans and well wishers for their continued affection. Merry Christmas and a happy new year to you all."
Congratulating Karina, film director Karan Johar tweeted : "My Bebo had a baby boy!!!!!!! Am so so happy!!!!!!! #TaimurAliKhan
A couple of months ago, Saif dismissed reports of a gender test as well as rumours that the baby would be born in London.
Kareena Kapoor, 36, and Saif Ali Khan, 46, married in 2012.
Saif Ali Khan has two children already with ex-wife Amrita Singh - daughter Sara and son Ibrahim.
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