Vanessa Hudgens Gives Birth, Leaves Hospital with First Baby

Vanessa Hudgens is officially a mother ... she gave birth to her first child, and it looks like things went well, because she's taking her bundle of joy home.

Check out these photos of Vanessa leaving the hospital Wednesday in Santa Monica ... where a nurse wheeled her out to her car with the baby swaddled in her arms.

The guy in the hoodie behind Vanessa is the proud father, Vanessa's MLB player husband Cole Tucker ... who seemed to have the added duty of getting their mountain of luggage out to their ride.

Cole's actually celebrating his 28th birthday today, and going home with his first child sounds like a pretty good bday present.

Unclear when Vanessa gave birth, but it's typical for mothers to spend anywhere from 1 to 3 days in the hospital after giving birth ... depending on the method of delivery, and how the baby's doing.

Vanessa and Cole started dating in 2020 before getting hitched in 2023 down in Mexico. She revealed her pregnancy this past March, showing off her growing baby bump at the Oscars.

VANESSA AND COLE TOGETHER

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No word on the baby's name or gender yet. We reached out to Vanessa's camp, but so far there's no word back.

Congrats and good luck -- first-time parenthood's always an adventure!