According to the site, Griffin will be joined by Rivers' daughter and FP producer Melissa Rivers, as well as co-hosts Giuliana Rancic and Kelly Osbourne. It's unclear as to whether fellow co-host George Kotsiopoulos will stay on as well.
TMZ reports that the show will no longer be aired on a weekly basis, but will air only during awards season and other special occasions as event programming.
A source close to the hit show tells Us Weekly that "Joan has always given her blessing to Kathy" and that she "wanted Kathy to be her successor."
"They talked about it many times," the insider says. "They have such a similar sense of humor and were the best of friends. Joan would have loved seeing Kathy on Fashion Police and she would have definitely approved."
Earlier this month, Griffin confirmed to Access Hollywood that she was offered the gig, but said: "I don’t know if the situation is correct at this time for me or right for me at this time."
Rivers tragically passed on Sept. 4 following an unplanned throat procedure at Yorkville Endoscopy in New York City on Aug. 28.