The America's Got Talent host will front a "candid, in-depth newsmaker interview programme" lasting for one hour from January.
"I have watched Larry King Live for much of the last 25 years, and dreamed of one day filling the legendary suspenders of the man I consider to be the greatest TV interviewer of them all," he said.
CNN's US president Jon Klein added: "Piers has made his name posing tough questions to public figures, holding them accountable for their words and deeds. He is able to look at all aspects of the news with style and humour with an occasional good laugh in the process."
King announced that he was ending Larry King Live in June. Morgan's unnamed show will air on CNN US and CNN-International and be based in New York.