The couple named the child August after the Facebook founder’s wife gave birth earlier this month.
In a post on the social network on Monday evening that attracted hundreds of thousands of “likes”, Mr Zuckerberg wrote: “Priscilla and I are so happy to welcome our daughter August!”
He then posted an open letter to their new-born baby below the announcement, explaining: “We wrote her a letter about the world we hope she grows up in, and also hoping she doesn’t grow up too fast.”
In it, they say they will “do everything we possibly can to make sure the world is a better place for you and all children in your generation”.
The Facebook CEO announced in March that a second child was on the way.
The couple already have a one-year-old daughter, Max, who was conceived following several miscarriages.
Here is the full letter from Mr Zuckerberg and Ms Chan to their baby:
Welcome to the world! Your mom and I are so excited to see who you will become.
When your sister was born, we wrote a letter about the world we hoped she and now you will grow up in — a world with better education, fewer diseases, stronger communities, and greater equality. We wrote that with all the advances in science and technology, your generation should live dramatically better lives than ours, and we have a responsibility to do our part to make that happen. Even though headlines often focus on what’s wrong, we still believe these positive trends will win out. We’re optimists about your generation and the future.
But rather than write about growing up, we want to talk about childhood. The world can be a serious place. That’s why it’s important to make time to go outside and play.
You will be busy when you’re older, so I hope you take time to smell all the flowers and put all the leaves you want in your bucket now. I hope you read your favorite Dr. Seuss books so many times you start inventing your own stories about the Vipper of Vipp. I hope you ride the carousel with Max until you’ve tamed every color horse. I hope you run as many laps around our living room and yard as you want. And then I hope you take a lot of naps. I hope you’re a great sleeper. And I hope even in your dreams you can feel how much we love you.
Childhood is magical. You only get to be a child once, so don’t spend it worrying too much about the future. You’ve got us for that, and we’ll do everything we possibly can to make sure the world is a better place for you and all children in your generation.
August, we love you so much and we’re so excited to go on this adventure with you. We wish you a life of joy, love and the same hope you give us.
Mom and Dad of August Facebook”