Meghan Trainor and Daryl Sabara are expanding their family ... because they have a baby girl at home ... and she was born via surrogate.

The singer and actor now have three children together ... and their newborn is named Mikey Moon Trainor.

In a social media post announcing her daughter, Meghan says ... "Our baby girl Mikey Moon Trainor has finally made it to the world thanks to our incredible, superwoman surrogate."

Meghan continues ... "We are forever grateful to all the doctors, nurses, teams who made this dream possible. We had endless conversations with our doctors in this journey and this was the safest way for us to be able to continue growing our family."

She adds ... "We are over the moon in love with this precious girl. Riley and Barry have been so excited, they even got to choose her middle name. We are going to enjoy our family time now, love you all."

Meghan posted a ton of photos of the baby at home and in the hospital ... so click through the gallery to see her growing family.

Congrats!!!