The new arrival is the third child for the 42-year-old jewellery designer, who is the daughter of Rolling Stones star Sir Mick and Bianca Jagger.
Jade Jagger and husband Adrian Fillary
Jade revealed her pregnancy on Instagram, posting a photo of her bump with the caption: "Happy to announce this granny is going to become a mummy, I’m 6 months pregnant xx double whammy this year."
Jade and Adrian tied the knot in July 2012 at a country mansion in the Cotswolds, proudly watched by her parents, Mick and Bianca Jagger.
Assisi's baby was born at the end of April, making her mother a grandmother for the first time and Sir Mick a first-time great-grandfather. The father is her boyfriend of three years Alex Key.
Jade Jagger and her daughter Assisi Jackson
It's unlikely that either of these children will be spoilt despite the family's great wealth.
Jade has explained in the past that she has never wanted to live off her father's money, saying she's "not a trust-fund child".
She added: "I think my father's got a healthy work ethic and, therefore, I think it just came with the part. You've got to look after yourself.
"It probably came more so from having kids and wanting to support them and look after them and give them the best I could."