John Dickerson, a veteran of CBS News and co-anchor of “CBS Evening News,” is leaving the network at the end of the year. Dickerson made the announcement in a social-media post Monday.

“Local news: At the end of this year, I will leave CBS, sixteen years after I sat in as Face the Nation anchor for the first time,” Dickerson, 57, wrote in a message shared via Instagram on Monday, Oc...