The scandal began after eight women told The Washington Post that Rose allegedly made unwanted sexual advances toward them, including groping them and making lewd phone calls between the 1990s and 2011.
On an interim basis, public TV stations will be able to air Amanpour's weekday public affairs program that originates on CNN International.
The half-hour "Amanpour on PBS" will air on New York's PBS station Thirteen on Monday in the 11 p.m. timeslot, and will be rolled out across PBS stations across the United States from December 11, the network said in a statement.
The program will air on PBS stations after it shows on CNN International.
BBC apologizes for Shashi Kapoor goof-up
Radio 4's Saturday Live presenter Aasmah Mir wrote: "I'm really annoyed about the BBC Shashi Kapoor thing. Some of the own members and stars of BBC criticized the error made on social media.
"Christiane Amanpour is a fearless and uncompromising journalist", Neal Shapiro, president and CEO of WNET, said in a statement.
The network is also finalizing plans for a second half-hour public affairs program to complete the hour. The host of that show will be announced at a later date.
"Charlie Rose" had run on PBS since 1994. "Charlie Rose is produced by Charlie Rose, Inc., an independent television production company".
"'Amanpour on PBS' adds to the long tradition of public affairs programming that has been a hallmark of public media for decades", PBS president and ceo Paula Kerger said.
Amanpour has earned eleven News and Documentary Emmy Awards, four Peabody Awards, two George Polk Awards, three duPont-Columbia Awards and the Courage in Journalism Award. CBS has yet to fill his anchor position on "CBS This Morning", relying for now on a combination of Vladimir Duthiers and Bianna Golodryga in the chair alongside Gayle King and Norah O'Donnell.