The 28-year-old Richie confirmed the engagement Monday during a taping of CBS' "Late Show With David Letterman." The show will air Friday at 11:35 p.m. EST.
Letterman asked, "You're not married yet, is that correct?" Richie replied, "We're not married."
Letterman then asked if she and Madden planned to get married. Richie said, "We actually recently are engaged, yes."
The 30-year-old Madden fronts the band Good Charlotte. The couple have a 2-year-old daughter, Harlow Winter Kate, and a 5-month-old son, Sparrow Midnight.
Richie has a new clothing line, Winter Kate, and shoe and accessories line, House of Harlow. She and Paris Hilton costarred on TV's "The Simple Life."
