Reality star Nicole Richie and singer Joel Madden have announced their engagement after having two children together.

Madden posted a message on the website Twitter on Monday that said he was engaged and "very happy," and Richie taped an appearance on television talk show "Late Show with David Letterman" on Monday in which she confirmed an engagement.

"We actually recently are engaged," Richie told Letterman.

Madden's Twitter post has since been removed, and Richie's appearance on Letterman is not scheduled to air until Friday.

Richie is the daughter of singer Lionel Richie and is best known for starring opposite celebrity heiress Paris Hilton in reality show "The Simple Life" from 2003 to 2007. Madden is the frontman for rock band Good Charlotte.

Richie and Madden have two children together, 2 year-old daughter Harlow and 5 month-old son Sparrow.

(Reporting by Alex Dobuzinskis: Editing by Jill Serjeant)

COPYRIGHT: (c) Reuters 2010. All rights reserved. Republication or redistribution of Reuters content, including by caching, framing or similar means, is expressly prohibited without the prior written consent of Reuters. Reuters and the Reuters sphere logo are registered trademarks and trademarks of the Reuters group of companies around the world.