Mr. Carlson, 47, whose father is a former president of the Corporation for Public Broadcasting, made his reputation as a conservative provocateur, though his style leans more toward William F. Buckley than Andrew Breitbart. Natty and quick-witted, though he has shed his once-signature bow-tie, Mr. Carlson splits his time between preppy enclaves like Georgetown and Maine, and was a magazine writer before turning to television punditry.

He has weathered his share of ignominious career moments, including an on-air dressing-down from the comedian Jon Stewart that led to the cancellation of “Crossfire.” An MSNBC showcase, “Tucker,” was canceled after less than three years, and he later made an ill-fated appearance on ABC’s reality show “Dancing With the Stars,” where he was cut in the first round.

He has also been routinely criticized by liberals and feminist groups for making remarks seen as patronizing or sexist. When his brother, Buckley Carlson, sent an obscene sexist email in 2015 to a spokeswoman for Mayor Bill de Blasio of New York, Tucker Carlson laughed off any concerns. Just last month, he ended a heated exchange with a Teen Vogue writer about politics by encouraging her to “stick to the thigh-high boots,” referring to her magazine’s focus on fashion.

Some left-leaning sites said Mr. Carlson had embarrassed himself; other right-leaning sites said that Mr. Carlson had embarrassed the writer.

Regardless of reception, the segment went viral, and even critics of Fox News concede that Mr. Carlson is skilled as a broadcaster. His 7 p.m. show, “Tucker Carlson Tonight,” routinely wins its time slot among the younger viewers that advertisers crave and whom Fox News, with its aging overall audience, is particularly keen to attract. In December, Mr. Carlson’s show beat Ms. Kelly’s program among viewers 25 to 54 years old, although Ms. Kelly was off for part of the month.

And even without the combative Mr. Ailes, Fox News remains an organization willing to ignore outside pressures. Hours after Mr. Carlson’s job was announced, the network said that it was awarding its correspondent Jesse Watters a weekly hourlong show on Saturdays. Last year, Mr. Watters used stereotypes about Asian-Americans in a segment filmed in New York City’s Chinatown, earning widespread criticism.

Mr. Carlson was one of several personalities rumored to be in contention for Ms. Kelly’s position, a group that included several female Fox News anchors. One of those anchors, Shannon Bream, will temporarily fill in for Ms. MacCallum in the mornings.