"NEWS NEWS NEWS !! I AM GOING TO BECOME A GRANDFATHER .. AISHWARYA EXPECTING .. SO HAPPY AND THRILLED !!!," the veteran megastar wrote on his Twitter account late on Tuesday.
Aishwarya Rai, 37, married Bachchan's actor son, Abhishek, 35, in April 2007.
The child will be their first and comes after weeks of media speculation in Indian gossip columns about the actress' fluctuating weight.
Bachchan Senior later said on the micro-blogging site that he was "overwhelmed" with the response to the news from followers and had received 2,843 Tweets of congratulation in just half an hour.
The pregnancy was confirmed earlier in the day, he wrote on his blog, bigb.bigadda.com, early Wednesday, adding: "There is joy and happiness around us," he added.
There was no immediate indication when the baby was due. The Bachchans - Amitabh, his actress wife Jaya, Aishwarya and Abhishek - are Bollywood's "first family" and have a fanatical following in India and around the world. His daughter, Shweta Nanda, has two children.