Everette's Brent Rupard and Wife Caroline Welcome First Baby, Son Wren Wesley: 'He's Just Perfect'

courtesy Brent & Caroline Rupard

Brent Rupard is a dad!

The musician - who is one half of the country/rock duo Everette - and his wife Caroline welcomed their first child, son Wren Wesley, on June 2, PEOPLE exclusively reveals.

The newborn was born in Nashville at 8:39 a.m., weighing 6 lbs., 5 oz.

"I still feel like I'm dreaming. When I first saw him, I felt like something clicked inside of me. Pretty wild," the new dad says.

"My wife Caroline is a superhero and is already the most amazing mom like I knew she'd be. I remember her mom asking me how she did during labor, and I said, 'She was like a Viking warrior in there,' " Brent adds.

courtesy Brent & Caroline Rupard

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courtesy Brent & Caroline Rupard

"Life still doesn't seem real with this little angel in our world. Every day we get to know him even more. He's just perfect," Caroline says.

As for how the couple chose their son's name, Brent explains, "We waited to name him until we met him, but instantly knew he was Wren Wesley. My middle name is Wesley and Wren was the only name on our list that felt like we didn't know that person yet," adding, "Wren is a type of bird that represents wit, ingenuity, cheerfulness and a free spirt. We're so thankful for this little ball of joy."

courtesy Brent & Caroline Rupard

RELATED: Everette's Brent Rupard and Wife Caroline Expecting Son: 'Terrified and Elated at the Same Time'

courtesy Brent & Caroline Rupard

Rupard and his wife Caroline revealed exclusively to PEOPLE in January that they were expecting their first child together.

The musician said Caroline shared the good news that they would be parents "after a long night of celebrating the release of" the band's debut album: Kings of the Dairy Queen Parking Lot, Side A.

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courtesy Brent & Caroline Rupard

"I was confused and had no idea what I was in for," said Rupard of his wife handing him an envelope with no further explanation.

"I opened the envelope to a simple message that read, 'Apparently, you are going to be a dad. Love, Jane' (her first name and what I call her)," the singer recalled.

While Rupard "had a dream" that their bundle of joy on the way was a girl, his wife's intuition said otherwise.

"Sure enough, she was right again! It's a boy!" he said. "We couldn't be more excited to welcome this baby boy into the world in early June."

courtesy Brent & Caroline Rupard

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"Like other first-time parents, I'm sure, we are completely terrified and elated at the same time," he added.

The couple tied the knot in Starkville, Mississippi, in October 2018, during an event the bride described in an anniversary tribute this past fall as a "festival."

"Two years of marriage already! I guess time does fly when you're having fun," Rupard wrote in his own two-year anniversary post, which featured a photo of his wife from the back, gazing out over a lake backed by mountains. "I love @carolinemelbyrupard and her beautiful spirit. I can't believe I have a front row seat to watch her shine. Happy anniversary!!"