The acquisition puts one of the country’s most traditional news institutions — the former home of Edward R. Murrow and Walter Cronkite — under the editorial guidance of a journalist who rose to fame in part by critiquing old-line media institutions that she deemed timid and untrustworthy. Ms. Weiss is also a stalwart champion of Israel, and her site frequently lambastes the perceived excesses of the so-called woke left.

Ms. Weiss, 41, has never run a TV network, and in her role will have influence over hundreds of producers, anchors and reporters around the world. She will report to David Ellison, Paramount’s chief executive, and work alongside Tom Cibrowski, the president of CBS News.