The former One Direction singer shared a black-and-white picture of the baby’s tiny hand clutching his tattooed finger with fans on Wednesday night.
He wrote alongside the sweet snap: “To try put into words how I am feeling right now would be an impossible task.
“The love I feel for this tiny human is beyond my understanding. Grateful to know her, proud to call her mine, & thankful for the life we will have together x.”
In a separate post to her more than 58 million Instagram followers, Gigi said she is “so in love” following the birth of her first child, revealing the baby arrived at the weekend.
Alongside a picture of the newborn holding Zayn’s thumb, she wrote: “Our girl joined us earth-side this weekend and she’s already changed our world. So in love.”
The 25-year-old model confirmed she was expecting in April, telling chat show host Jimmy Fallon she and Zayn were “happy and grateful for everyone’s well wishes and support”.
The new arrival came hours after Zayn teased his first new music since 2018 album Icarus Falls. He tweeted a short section of the track Better, revealing it will arrive on Friday.
Zayn, 27, is the third member of One Direction to become a father.
Louis Tomlinson welcomed son Freddie in January 2016 while Liam Payne has a three-year-old son, Bear, with singer Cheryl.
Los Angeles-born Gigi and Bradford-born Zayn have been dating on and off since late 2015.
Last week, Gigi’s father Mohamed shared a message on social media for the unborn baby.
“Hello little grandchild, it is me, my heart as happy as can be,” he wrote.
“I wish for you the sun & moon, I wish for you a happy time. Know that grandpa’s always here, I’ll do anything, anything for you, my dear.”