"[We're] having a little boy [and] we're going to name him Caleb," he told PEOPLE exclusively at the show's season-seven finale Wednesday night.
This is the second child for Bice and his wife, Caroline Fisher, who are already proud parents to 2-year-old Adian Michael.
"[Caleb] is a good biblical name," Bice added at the event, held at the Nokia Theater. "We stuck with that with both kids – good Irish and good biblical names ... We're just blessed to have such a beautiful family."
The rocker dad – who opened up his own record label, Sugar Money, last year and released the album See the Light – has no complaints about life as an Idol runner-up. (David Archuleta, take note!)
"You know, all my dreams have come true," Bice gushed. "To be able to be a dad and got out and perform shows and do what we love for a living, man ... there's nothing better!"