In a statement, Hilton said the parting of ways was "no big secret," E! Online reported Thursday.
"I will not go into the details of what happened. All I will say is that Nicole knows what she did and that's all I am ever going to say about it."
Reports have been swirling since last summer that Hilton and Richie were on the outs following some off-camera squabbles while shooting the second season of the FOX-TV show.
"The Simple Life: Interns," the third season, debuted with the series' best-ever ratings of 13.3 million viewers. Although those numbers have steadily declined in recent weeks, the show averages a healthy 10.2 million on Wednesdays opposite ABC's new hit, "Lost."