8:50 AM PT -- Chris just officially announced the big news and revealed their baby girl's name ... Lyla.
He says ... "We are beyond thrilled to announce the birth of our daughter, Lyla Maria Schwarzenegger Pratt. We couldn’t be happier. Both mom and baby are doing great. We are extremely blessed. Love Katherine and Chris."
Chris also shared a couple Bible verses, including Psalm 126:3 -- "The LORD has done great things for us, and we are filled with joy."
The news came after a photographer spotted Patrick Sunday and congratulated him on becoming an uncle and then asked how Katherine and the baby are doing. PS responded, "Doing great, just got her a little gift." He then made it even clearer by showing the photog the gift, wrapped in a pink ribbon.
So, Katherine and Chris had a girl!!! It's Katherine's first child and Chris' second. He and ex-wife Anna Faris have a son, Jack. ET first broke the story.