The baby boy, who will go by the name Shepherd, weighed in at 8 lbs, 4 oz. "I am so overjoyed," the proud papa, 22, tells PEOPLE. "There is not an audience or concert that could ever stand up to the feeling of meeting your baby for the first time."

New mom Kate, 24, is equally happy, saying, "Shepherd is the most wonderful gift we could ever receive. We're already enjoying every second of this great adventure."

Though Shepherd is only a day old, he's already got a built-in playgroup: Cousins Ezra, 5, Penelope, 3, and River, 20 months (middle Hanson brother Taylor and his wife Natalie's children) and Everett, 1 (eldest Hanson brother Isaac, and his wife Nikki's son).

But Shepherd won't be the baby of the family for long: Isaac and Nikki will welcome their second child next month.

"It will be really fun to see [the] little ones grow up together," Zac told PEOPLE in November. "I know watching them is going to inspire a lot of music."

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