Veteran TV journalist Rose, 76, was sacked by CBS in November after being accused by more than 10 women of sexual misconduct. The show is now hosted by Norah O'Donnell and Gayle King. That sets him apart from ABC "Good Morning America" host George Stephanopoulos, who continues to host ABC's "This Week" on Sundays.
Mr. Dickerson - whose mother, Nancy Dickerson, became in 1960 the first female correspondent at CBS News - plans to move to NY and leave "Face the Nation", which he joined in 2015.
He will be counted on to help CBS keep delivering its most-watched morning news show in decades.
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.
James Franco and Tommy Wiseau: Winning Best Actor for the Worst Movie
That was provided, appropriately enough, by James Franco , Tommy Wiseau and the inside-out making-of tale " The Disaster Artist ". He said to his best friend Greg [Sestero], 'The Golden Globes? "I won the the award, I'm talking", laughed another.
"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.
And he has demonstrated a natural chemistry with King and O'Donnell when he filled in.
"This Morning" has the smallest audience of the three main morning shows on USA broadcast television with a daily audience of about 3.6 million. CBS News has not announced a replacement for Chaggaris. The "Today" show decided upon officially creating an all-female co-hosting team after Matt Lauer was forced out - a historic move made easier because viewership of the Hoda Kotb-Savannah Guthrie program actually increased in Lauer's absence.
PBS and Bloomberg, which broadcast the "Charlie Rose" show, also said they were terminating their relationships with Rose and canceling distribution of his programs in the aftermath of the misconduct allegations.
Dickerson is expected to continue his duties as Face the Nation moderator.