The journalist John Dickerson is a Washington creature to his core: a presidential historian, repository of political trivia and scion of a glamorous Beltway family whose party guests regularly included Kennedys, Johnsons and Reagans.

Now, Mr. Dickerson, who until recently was better known as a political correspondent than as the host of the CBS Sunday show “Face the Nation,” is leaving the capital for a new job in New York: morning TV host.

CBS said on Tuesday that it had chosen Mr. Dickerson, 49, to replace Charlie Rose as the third member of the of “CBS This Morning” team, a spot left empty since Mr. Rose was fired in November after allegations of sexual harassment. Mr. Dickerson is to join the lineup of Gayle King and Norah O’Donnell, who have carved a niche as a news-driven morning team.

A genial on-air presence who speaks in a light Virginia accent, Mr. Dickerson received praise at “Face the Nation,” which he joined in 2015, for his rigorous, and at times academic, approach.