The couple, who tied the knot Thursday evening, began dating 10 years ago when Regina worked for him on his show
According to transcript released to Us by the Late Show rep, Letterman said: "On Thursday, at 3 p.m., March 19, 2009, at the Teton County Courthouse in Choteau, Montana, I was married to Regina Lasko.”
"Regina and I began dating in February of 1986, and I said, 'Well, things are going pretty good, let's just see what happens in about ten years...'"
"…I had avoided getting married pretty good for, like, 23 years, and I -- honestly, whether this happened or not -- I secretly felt that men who were married admired me…like I was the last of the real gunslingers, you know what I'm saying?'" he joked.
They welcomed their son Harry into the world on November 3, 2003, but according to David, his son hasn't inherited his fathers sense of humor.
"Mommy has to tell him a lot that I'm just teasing," he joked.
Letterman was previously married for seven years to his college sweetheart Michelle Cook. They divorced in 1977.