The CBS News boss noted that Ms. King brings qualities to the network that it did not have in its previous golden age, when “60 Minutes” made stars out of its correspondents. “Gayle has evolved as someone we’ve not ever had at CBS in that vein,” Ms. Zirinsky said. “Sure, we’ve had the Mike Wallaces and the Ed Bradleys, but Gayle has this humanity, relatability, this curiosity. She’s smart and people trust her.”

The CBS News president also pointed to Ms. O’Donnell’s recent on-air performances during the congressional testimony of Michael D. Cohen and the release of the report from the special counsel Robert S. Mueller III. “Norah is a game changer,” Ms. Zirinsky said. “Watching her anchor the Mueller report, watching her anchor when Cohen testified — Norah’s got a big brain. She is such a dynamic broadcaster.”

While Ms. Zirinsky deliberated on remaking CBS News, the tabloids were filled with speculative articles on who would stay and who would get the boot. Many of the stories included rumors of tensions between Ms. O’Donnell and Ms. King, which the two dismissed on Monday’s broadcast of “CBS This Morning.”

“I have no beef with you, you have no beef with me,” Ms. King said to her colleague. And Ms. O’Donnell called Ms. King “my work B.F.F.”

Ms. Zirinsky said the people in the division she oversees were “relieved” that the waiting period had finally come to an end. “Now we can put teams together and build armies and really become battle-ready,” she said.

In addition to the personnel changes, Ms. Zirinsky has decided to move “CBS Evening News” from its longtime Manhattan home to Washington, in the hope that the new location will attract more viewers and set the show apart from rival newscasts on NBC and ABC.

Ms. O’Donnell was born in the nation’s capital, and Ms. Zirinsky described her as someone who is “wired in Washington,” adding, “I really want to make clear that this show is not staying inside the Beltway. When you want to cover the story, what do you do? You get as close as you can. What’s happening in Washington over the next year really impacts the rest of the country. This is our way in, to distinguish ourselves, so that we can look at the country and really reveal America to itself.”