The TV host tied the knot at a courthouse in Montana on Thursday and announced the big news at Monday’s taping of CBS’ “Late Show” in Manhattan.

“I had avoided getting married pretty good for, like, 23 years,” he said. “I secretly felt that men who were married admired me – like I was the last of the real gunslingers.”

The family’s truck got stuck in the mud en route to the courthouse, he said. Jeepers. Letterman “walked two miles back to the house in 50 mph wind. It’s not Beverly Hills — it’s Montana.”

“And the whole way, I’m thinking, ‘See … you try to get married and this is what happens.’”