Rodgers, 30, spoke about the relationship for the first time and said he did not want public scrutiny, but is trying to adjust with it, reported Ace Showbiz.
"I'm real happy in my relationship. And I understand what comes with it. And the last couple years, I've learned a lot about perspective and what's important," he said.
Reports of his romance with Munn, 33, emerged in May.
"It's not what I signed up for, but I understand it comes with the territory. There's always going to be attention or scrutiny, and you can either... Embrace it or you can lock yourself away," Rodgers said.