Fox News tapped veteran journalist and commentator Tucker Carlson to replace Megyn Kelly in one of its most prominent time slots, underscoring that the cable news network has no intention of moving away from its conservative roots.

Mr. Carlson, who had recently begun hosting a 7 p.m. show on Fox News, will take over the 9 p.m. time slot from Ms. Kelly, a star anchor who announced this week that she is leaving for NBC News after a 12-year career at Fox. Mr. Carlson takes over on Monday.

The 47-year-old rose to national prominence as the co-host of the CNN show “Crossfire,” where he represented the political right until the show’s cancellation in 2005. He has written for a variety of media outlets over the years and co-founded the conservative site the Daily Caller.

Picking an established anchor on its own network was a safe move for Fox News. Mr. Carlson has done well at 7 p.m. since replacing Greta Van Susteren in November. His average audience of 2.8 million viewers beats both CNN and MSNBC combined.

MSNBC announced Thursday that Ms. Van Susteren will be joining the network to host “For the Record with Greta,” providing news coverage and analysis at 6 p.m. on weeknights. Her show also starts on Monday.