Mr Zucker was abruptly oustered earlier this month after he was revealed to have been in an undeclared relationship with his second-in-command, Allison Gollust.
His firing came as part of an investigation into former primetime anchor Chris Cuomo giving advice to his brother Andrew during the former New York Governor’s sexual harassment scandal.
Ms Gollust later resigned from CNN after it emerged she had discussed interview topics with Andrew Cuomo prior to his appearances on the network.
Mr Licht, who has worked as a producer in television news for more than 20 years, created MSNBC’s Morning Joe and worked on CBS This Morning before joining the Late Show as show runner and executive producer in 2016.
He is expected to take over after Discovery completes it merger with CNN parent WarnerMedia sometime this spring, according to CNN media correspondent Brian Stelter.