Rai is married to actor Abhishek, Mr Bachchan’s son. This will be the couple’s first baby.
Often called the “queen of Bollywood”, Rai, 37, married Bachchan in 2007, forging the ultimate Bollywood dynasty.
She first charmed the nation at just 21, winning Miss World in 1994. She has acted in several Hollywood films too.
“News news news!! I am going to become a grandfather. Aishwarya expecting. So happy and thrilled,” Mr Bachchan tweeted on Tuesday night.
The actor later wrote that he had received “2,843 tweets in the first half hour” and that he was “overwhelmed with wishes and blessings”.
It’s not yet know when the baby is due.
Rai was the first Indian actress to sit on the Cannes jury in 2003. She has also appeared on the cover of Time magazine as the global face of Indian cinema.
Because of her popularity in India and outside, she has long been the face of cosmetic giant Loreal and high-end Longines watches.