"All I ever hoped for was one boy and to have two, it's going to be fun. I've already got new fishing spots picked out for us," Bryan, 34, tells PEOPLE exclusively.
The singer called from his cell phone while at a local Sonic where he was picking up a lemon berry slush for wife Caroline, 30.
"I had planned to buy her a little present today but then the baby came early, so the slushie will have to do it for now," he explains with a laugh.
The singer’s other fishing buddy, elder son Bo, 2, hasn't met his little brother yet.
"He was playing on the slide at the Chick-fil-A with his nanny when we called to tell him – I think he was more concerned with his chicken nuggets than the baby at the time," Bryan says.
But he may change his tune when he meets Tatum, whom the country star says looks "pretty much like a carbon copy of Bo."