Sharing the happy news with HELLO! on Friday, the couple said: "The moment she was born we fell utterly in love with her. We can't believe how lucky we are to have her in our life and feel overwhelmingly happy."
They also released two adorable photos of their new bundle of joy - one image showed Natalie's hands holding her daughter's feet, while the other was of her newborn's hand.
WATCH: Natalie and Zafar Rushdie share their baby joy
Their baby daughter is the first grandchild for Zafar's famous father Sir Salman Rushdie, the esteemed novelist and Booker Prize winner who is now based in New York.
The new parents, who have been married since June 2016, announced their pregnancy news with HELLO! back in May.
Natalie Rushdie has given birth to a baby girl
At the time, Natalie revealed she hopes she can rope in father-in-law Salman to help with homework when the time comes. "He just knows everything about everything so I really think, hopefully, he can give all of his knowledge to our child," she shared.
Lockdown did not affect their ability to toast the happy news with their nearest and dearest in person. Since their first scan, which took place just before the social distancing measures came into play the first time round, Zafar was unable to accompany Natalie to her hospital appointments.
This is the first child for the couple
"She's either Facetimed me in for a live 'broadcast' of the scan or videos it to show me afterwards," he explained. "Five months is a long time. The world has changed a lot in the last two months so… hopefully, things will be better than they are now. I would feel really, really disappointed not to be there."
Natalie, who suffered from morning sickness from day one and lost a stone in weight, added: "Movies depict this idea that pregnancy is all wonderful and glowing but really, it's hard work… but throughout this pregnancy Zaf has been so calm and reassuring."
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