February 09, 2018 at 08:00 AM EST

Aaron Paul has a new pretty baby bird to love!

The Breaking Bad alum, 38, and his wife Lauren announced the birth of their first child on Instagram Thursday. “There are no words that will ever be able to explain what just happened to my heart,” Lauren captioned photos of the newborn baby girl.

“My heart,” the actor simply captioned his black and white portrait of his daughter’s foot.

The couple, who tied the knot four years ago, first announced they were expecting back in September. “Hey everyone. Look what I did,” Paul, 38, wrote alongside a photo of Lauren cradling her baby bump.

He continued, “Words can’t express how excited I am that this little one has entered our lives. Just thought it was time I would share this beautiful news with all of you.”

Not too long after, Lauren revealed that their impending bundle of joy would be a baby girl. However, when it came to choosing a moniker for their daughter on the way, the pair knew they wanted to wait.

“We have a few, a few names,” Paul previously told PEOPLE. “If one of us didn’t like one of the names it never made it into the pile. We have a handful of names and we’re going to name her once we meet her.”

Throughout the pregnancy, the two have been sharing snaps of Lauren’s baby bump on social media — including a sweet post by Paul in honor of his wife’s 31st birthday.

“Happiest of birthdays to this mother to be,” Paul wrote on Dec. 8 alongside a photo of Lauren pulling up her sweatshirt to get a better shot of their growing daughter.

“Can’t wait for this precious little baby girl to be in our arms my love,” added the actor. “What a gift you are to this planet. I love you thru the stars and back. Enjoy the day.”

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