October 01, 2014 08:30 PM

Splash News

Mila Kunis and Ashton Kutcher are parents!

The couple welcomed their daughter at 1:23 a.m. on Wednesday, Oct. 1, and Kutcher revealed her name on his website Thursday.

“Mila and I would like to welcome Wyatt Isabelle Kutcher to the world. May your life be filled with wonder, love, laughter, health, happiness, curiosity, and privacy,” he wrote.

Speaking of privacy, the actor’s post included photos of several different babies. “Can you guess which one is ours, or does it really matter?” he wrote. “All babies are cute.”

“She’s here and healthy,” a source said shortly after Wyatt’s arrival. As for her name, only Kutcher’s mother knew it ahead of time, a source close to the actor tells PEOPLE. The couple really liked unisex names, adds the Kutcher source, and the other names they considered were unisex as well.

Kunis, 31, and Kutcher, 36, have had an eventful year.

In February, their engagement was confirmed, followed by their baby news in March.

Soon after, Kunis told Ellen DeGeneres that she was planning on an epidural-free birth. “The hospital that I’m going to be laboring in does a midwife, you know, doula type of thing,” she said.

“I’m going to do it as all natural as I possibly can unless there’s an emergency or something that should go wrong. I did this to myself, I might as well just do it right. I wanted this!”

The former That ’70s Show costars, who were first rumored to be dating in April 2012, have been happily preparing for their baby girl’s arrival, with Kunis attending prenatal Pilates and yoga throughout her pregnancy and Kutcher doting on her.

“Ashton is super excited,” his Two and a Half Men costar, Jon Cryer, recently told PEOPLE. “Ashton has even been excited every time we had a child actor on set. He loves kids and could not be more stoked to have a child.”

As for Kunis, she told W magazine in July that she was eager to scale back her work commitments after becoming a mom.

“I have never wanted to be the person who only has business on her mind,” she said. “To me, this job has always been a hobby that turned into a great profession, but I don’t eat and breathe acting. I’m sure Meryl Streep has a very different point of view. But I’m excited about being a full-time mom.”

TMZ.com was first to report the happy news.

— Michelle Tauber with reporting by Aili Nahas and Julie Jordan

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