Murphy welcomed a son, Logan Phineas Miller Murphy, with husband David Miller on Christmas Eve.
© PA Images / Chris Pizzello/AP
The baby boy was born at 9.47am, weighing in at 6lbs 6oz, according to People.
The new addition to the family measured 21 inches long.
The American Horror Story creator and New Normal showrunner previously dropped clues that he would be starting a family soon.
"I think I'll be incredibly fun and overwhelmed and all about manners," he said.
"I'm excited to have somebody or something come in and say, 'Really? I don't care what you think. I'm going to do what I want'."
It is currently unknown whether Logan was born via a surrogate or was adopted.
