Rose's co-hosts on "CBS This Morning", Norah O'Donnell and Gayle King, on Tuesday voiced their dismay at the allegations.
The eight women told the Washington Post that Rose made unwanted sexual advances toward them, including groping them and getting naked in their presence.
"I deeply apologize for my inappropriate behavior", Rose said Monday.
Rose has co-hosted the morning show since 2012, and it has gained in the ratings against its better known ABC and NBC rivals with a newsier approach.
Rose routinely landed the biggest names in worldwide politics, entertainment and letters for his interview show "Charlie Rose", which was broadcast on PBS and Bloomberg TV.
PBS also released a statement, saying it had terminated its relationship with Rose - whose interview show first aired on its network in 1991 - and that it had now cancelled distribution of his programs.
Colbert later pulled an excerpt from the Washington Post bombshell that had one accuser claim that she was invited to his beach house changed out of his wet clothes and into a bathrobe wearing nothing underneath.
"Well, you did your job this morning, I did my job today", he said, earning applause from the audience.
David Cassidy In Critical Condition ... Organs Failing
His relationship with his father, who he likened to a "boot camp sergeant" was less harmonious, Cassidy told The Guardian in 2012. David Cassidy , the 70s heartthrob who played Keith on " The Partridge Family ", died Tuesday at the age of 67.
"A short time ago we terminated Charlie Rose's employment with CBS News, effective immediately", CBS News President David Rhodes said in an internal message that was shared with media. None of the women worked for CBS or PBS, according to the report, and PBS, CBS and Bloomberg all told the newspaper that "they have no records of sexual harassment complaints about Charlie Rose". This followed the revelation yesterday of extremely disturbing and intolerable behaviour said to have revolved around his PBS program. "I really am still reeling", she said.
One woman said Rose fired her after learning that she had confided in a friend about his behavior.
"I was wincing at your monologue though, Stephen", she scolded.
"It is systematic and pervasive, and I've been doing a lot of listening and I'm going to continue to do that", she said. "What do you say when someone you deeply care about has done something that's so frightful?"
Gayle King opened up about Charlie Rose's sexual harassment allegations on "The Late Show" Tuesday night.
"He doesn't get a pass because I can't stop thinking about the anguish of these women; what happened to their dignity, what happened to their bodies, what happened to maybe even their careers".
The women also described how Roses staff brushed off their complaints about his behavior as just Charlie being Charlie.