"One week with our sweet boy! Madden Matthew Ertz you are so loved," Ertz wrote on Instagram. "Beyond grateful to be your Dad. @julieertz and I can't even put into words how blessed we are to be your parents."

In the pic, Madden is wearing a cream-colored hat and appears to be resting peacefully, next to a name tag that shares the date (Aug. 11) and time he was born ... as well as his height and weight.

The NFL tight end and USWNT star -- who've been together for nearly a decade -- announced back in April they were "adding to our starting lineup," and they've been super stoked about it ever since.

Zach and Julie have been married for five years ... and took romantic photos of the Super Bowl champ kissing Julie's growing tummy to accompany the BIG news.

It's a great name for baby Ertz -- although it's unclear if the late legend John Madden served as the inspiration.

Nevertheless, the two seem to be all smiles since Madden's arrival ... and we already know they're going to be fantastic parents.