During the interview, which was taped Monday, Letterman asked Richie if she was married.
"We actually recently are engaged, yes," Richie said.
"You are engaged?" Letterman replied. "Oh, congratulations, that's nice. ... A lot of people will have children and then they don't want to rush right into the marriage -- you know, they wait 'til the kids get out of college, then they get married."
Richie and Madden are the parents of a daughter, Harlow Winter Kate, 2, and a son, Sparrow James Midnight, 5 months.
Earlier in the interview, Letterman asked Richie, "When you have the kids, everything changes, doesn't it?"
"It does," Richie said. "It sounds cheesy to say, but it does. Your whole life changes and your priorities change 100 percent."
"In a great, great way," Letterman said.
"In the best way possible," Richie replied.