Meet Grayson Lane! Travis Stork and Wife Parris Introduce Newborn Son: 'I Love Being a Dad'

Travis Stork is ecstatic about his newest title: Dad.

The Doctors host, 48, and wife Parris share the first photos of their 1-week-old son Grayson Lane in this week's issue of PEOPLE, where the proud new father also opens up about one of the more "unsettling" parts of the experience of welcoming their new addition.

"The first night, when he was whisked away to the ICU with breathing problems, was one of the more unsettling nights of our life," says Stork. "To now have him home with us and doing well makes us even more thankful."

"Parris and I feel so very blessed to have Grayson as our son," he adds of himself and his wife, 27. "We've started to figure each other out. Even our dog, Charlie, now understands our new family."

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Stork describes his "little stud" of a son as "a happy baby" — though he admits he's "definitely biased."

"I love being a dad!" says the PEOPLE Health Squad member. "Just as much, I love his unique connection with his mother and watching them together makes me smile wider than I thought possible."

"If this all sounds cheesy, I get it. I have a lot of oxytocin flowing through my veins!" Stork jokes.

Baby Grayson arrived on Wednesday, June 17, at 1:10 a.m., weighing 8 lbs., 6 oz. He measured 22 inches long.

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"We are so excited and blessed to welcome Grayson Lane into this world," Stork told PEOPLE at the time. "He had a bit of a rough go of it, initially requiring his first night be in the NICU, but he's doing great."

"He's sweet and peaceful and his daddy can't wait to hold him for the first time once he's out of the ICU!" he added.

Sharing a photo of the new mom and baby to Instagram, Stork wrote of his son, "He had some trouble breathing due to meconium in his lungs so he's still in the ICU but he's doing great! He's so very sweet and his mom was an absolute rockstar. I know everyone says when you see your first born it changes you. For me, it was seeing Grayson together with his mother. That's my family. My team. And I couldn't be more blessed!"

For more from Travis Stork, pick up the latest issue of PEOPLE, on newsstands Friday.