The Camilla With Love designer shared the news via Instagram on Tuesday.
"Our little Luna Gypsy entered the universe on Sunday afternoon and into our arms. Welcome darling girl, you are so very loved by your mummy and daddy 🌙 xxC," she captioned a photo cuddling up to her daughter.
Luna Gypsy is the first child for Franks, whose Caftans have been worn by celebrities including Beyoncé, Oprah and Sofia Vergara.