Dorenbos -- who crushed it on "America's Got Talent" -- was diagnosed with an aortic aneurysm during his physical for the Saints last week ... which prompted the emergency surgery.

Eagles head coach Doug Pederson gave an update on his ex-player's condition, saying, "Everything went well yesterday with surgery and he's resting comfortably."

"Just wish him and his family well, our prayers are with him and hope for a speedy recovery."

The NFL vet shared a video of his friends and family before going under the knife, saying, "Thank you to my beautiful amazing wife, my family, my friends and videos like this. This brought out some tears. I feel the love and support."

Get well soon, Jon!