The 27-year-old actress shared a sweet snap of the new arrival on Saturday revealing they had named her Delilah Ruby Sinclair.
She caption the black and white image of herself in a birthing pool cradling the new born: “Our beautiful precious daughter Delilah Ruby Sinclair was born yesterday on the 22nd of June at 5.18pm weighing 6lbs 15oz.
"I had a very quick labour, a water birth with just gas and air, absolutely besotted so in love.”
Delilah, who was born at Queen Elizabeth University Hospital in Glasgow, is a little sister to two-year-old Matilda.
Flanagan, who plays Rosie Webster in the soap, shared a second picture of Matilda grinning and holding her little sister.
She then posted a snap of herself in black leggings and a hoody cradling Delilah and wrote: “Cloud 9”.
Celtic footballer Sinclair posted an adorable picture of himself kissing his new daughter's forehead.
He proposed to his actress girlfriend in Disneyland back in May.