The Little Mix singer announced on Sunday that she and Alex welcomed their new arrival on Saturday.
Perrie also shared black and white pictures of the baby’s hands and feet as she shared the news with fans on Instagram.
“Welcome to the world baby 21/08/21,” she captioned the pictures.
Earlier this year, the Little Mix stars revealed the adorable story behind how they both found out they were pregnant.
In a TikTok interview, Perrie said: “We were on a work Zoom and we were chatting about things that were coming up in our schedule because in Little Mix we are blocked out two years in advance.
“I was thinking, ‘I won’t be able to do that’.
“I messaged my manager and she called me and said, ‘You’re pregnant’.
“I was like, ’How do you know? And she said, ‘Because I am pregnant’. Then she said, ‘Can I add someone to the call?’”
Perrie continued: “I just heard this voice that said, ‘Perrie! You too!’ And then we just cried our eyes out. We couldn’t believe it.
“What timing! It wasn’t planned.”