Jade Jagger, 42, confirmed her daughter Assisi Jackson is expected to give birth in the New Year, saying: "It is true. I am going to be a grandmother."
Although there have been rumours Ms Jackson, 21, was pregnant, this is the first time the news has been confirmed by a member of her family.
In the article to be published in The Sunday Times' Style magazine next weekend, Jagger said her father shrugs off suggestions he is getting too old for rock 'n' roll.
She added: "I think making Mick a grandfather obviously had a big impact whereas, now, making him a great-grandfather is no longer particularly fascinating."