The couple welcomed its first child in a hospital in Mumbai, India and shared the news in a press release hours later.
"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," the stars state.
Saif, 46, is also father to a son and daughter from his first marriage to actress Amrita Singh. They divorced in 2004, and he went on to marry Kareena, 36, in 2012.
The baby was born into Bollywood royalty. Saif's parents are retired actress Sharmila Tagore and former Indian cricket captain Mansur Ali Khan Pataudi, while Kareena's dad, Randhir Kapoor, grandfather Raj Kapoor, and great-grandfather were all involved in the Indian film industry.