A boy was born to Bollywood's leading couple Saif Ali Khan and Kareena Kapoor on Tuesday, the stars announced in a statement.

Kareena delivered the baby in a hospital in Mumbai, relatives of the actors 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," the couple said in a statement, according to broadcaster NDTV.

"To have a child now completes us. There is something about a baby that is kind of half mine and half of hers, so, it's a nice feeling," Saif said earlier on Monday.

The pair, dubbed Saifeena by Indian press, were married in 2012 in Mumbai. Taimur is the couple's first child.

Khan, 46, is the son of late Indian cricket captain Mansur Ali Khan Pataudi and Sharmila Tagore, an actress prominent in the 1960s.

Kareena, 36, is part of a Kapoor family which has held centre stage in Bollywood for decades.

Bollywood celebrities took to social media to congratulate the couple.