In a memo to colleagues that was obtained by The New York Times, Mr. Zucker wrote that his relationship came up during a network investigation into the conduct of Chris Cuomo, the CNN anchor who was fired in December over his involvement in the political affairs of his brother, former Governor Andrew M. Cuomo of New York.

“As part of the investigation into Chris Cuomo’s tenure at CNN, I was asked about a consensual relationship with my closest colleague, someone I have worked with for more than 20 years,” Mr. Zucker wrote. “I acknowledged the relationship evolved in recent years. I was required to disclose it when it began but I didn’t. I was wrong.”

“As a result, I am resigning today,” he wrote.