The musician's daughter Jade Jagger's eldest daughter Assisi is due to give birth in the new year.
It will be the first baby for the 21-year-old socialite and her partner Alex.
"She and Alex are thrilled and broke the news to their immediate families last week," a source told the Mirror. "Jade was a little taken aback at first, not least because it means she will be a grandmother by the age of 42."
"She's expecting some ribbing from her showbiz pals," the source added. "Mick is delighted and has no qualms about being a great grandfather. He's been joking about becoming a great, great, grandad and still performing!"
The baby will be the latest addition to the large Jagger clan.
Sir Mick is father to seven children aged between 14 and 42 by four women.
Mum-to-be Assisi with her grandmother Bianca Jagger and sister Amba
His eldest child Karis was born in 1970 following a fling with model-actress Marsha Hunt while Jade's mum is Mick's first wife Bianca.
The Satisfaction fathered four children – Elizabeth, James, Georgia May and Gabriel – in his nine year marriage to model Jerry Hall.
His youngest son Lucas came after a fling with brief fling with Brazilian model Luciana Gimenez.
His grandchildren are Assisi and her sister Amba and Karis' two children.