The Sky News political editor was involved in the fiery exchange in a live interview two weeks before the General Election.
He told the BBC Radio 4 Today programme: “Of course I regret showing a little bit more temper than was necessary.”
Campbell had accused the broadcaster of treating then-prime minister Gordon Brown as “dead meat” and said he was “obviously upset that David Cameron is not Prime Minister”.
A clearly angry Boulton responded: “I’m not upset. You keep casting aspersions... Don’t keep telling me what I think. I’m fed up with you telling me what I think, I don’t think that.”
Boulton told Today: “Here we had an unelected person who actually didn’t even have a job in the Labour team who was coming out and, before the Cabinet had met, telling us what the Government was going to do.
“And once I tried making these points to him he turned nasty and attacked my integrity.”