Sources tell us the actress gave birth Sunday in L.A. to a healthy boy, whom she and the father, her BF Garrett Hedlund, have named ... wait for it ... Rhodes!!! We're told he weighed in right around 9 lbs and both Baby and Mama Bear are doing great after the delivery.

Emma hasn't been shy about showing off her baby bump either these past few months -- in fact, she just posed for a nice holiday shot a few weeks ago. She was also spotted out and about last Wednesday looking ready to pop.

This is Emma's first child, Garrett's too. The couple were first linked together shortly after Emma broke off her engagement with Evan Peters in the spring of 2019. While reports said they were keeping things caj at first ... the relationship clearly sped up, because it wasn't long before word of Emma's pregnancy surfaced, which she confirmed in August.

Nothing like a whirlwind romance to bring about a new life. Congrats to the whole family!!!