Veteran TV journalist Rose, 76, was sacked by CBS in November after being accused by more than 10 women of sexual misconduct.
"John's impressive track record and strong all-around journalism extends our commitment to real news coverage every morning at CBS News", Rhodes said in a statement.
Dickerson took over the anchor's chair on "Face the Nation" in June 2015.
"Today is our sixth anniversary". Nothing official yet from CBS News, though sources are talking and word spread quickly.
"This is a new beginning with an old friend", O'Donnell said. "Every time I've been on the show, I haven't wanted the conversation with Norah and Gayle to end when my segment does".
Virginia native Dickerson, 49 - son of pioneering newswoman Nancy Dickerson - was a correspondent for Time and Slate before joining CBS in 2009 as an analyst before becoming political director.
United States television channel CBS announced today that its shamed millionaire news anchor, sacked for alleged sexual harassment, had been replaced by another man after its higher-rated rival appointed a woman. King and O'Donnell also released statements revealing their excitement to welcome Dickerson to the team.
Dickerson is expected to continue his duties as Face the Nation moderator.
NBC News had a similar morning show problem with Matt Lauer, giving him the sack from Today show only about a week after CBS News jettisoned Rose.