The former One Direction singer posted a black-and-white picture of his daughter's tiny hand clutching his tattooed finger - model Hadid shared a similar post.
Writing on Twitter, 27-year-old wrote Malik said: "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, 25-year-old Hadid said she is "so in love" following the birth of her first child.
The baby girl arrived at the weekend.
Alongside a picture of the newborn holding Malik’s thumb, Hadid wrote: "Our girl joined us earth-side this weekend and she’s already changed our world. So in love."
With more than two million likes between them for the posts, the couple's A-lister friends congratulated them on the new arrival.
Fellow model Hailey Bieber said: "Welcome babygirl! So happy for you guys."
Actress Emily Ratajkowski wrote: "Congratulations Gigi & Zayn!!"
Model Olivia Culpo said: "Ahhhh!!!!! HUGE congrats!!!!! I can’t wait to meet this angel."
And Kourtney Kardashian shared a series of heart emojis.
US model Hadid confirmed she was expecting in April.
She told chat show host Jimmy Fallon at the time that she and Malik were "happy and grateful for everyone’s well wishes and support".
The new arrival came hours after Malik 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.
Malik is the third member of One Direction to become a father.
Los Angeles-born Hadid and Bradford-born Malik have been dating on and off since late 2015.
Last week, Hadid’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."