Gibson, who has more than 20 years' investment banking experience, has been Deutsche Bank's co-head of investment banking in New Zealand and Deutsche Craigs. He has also advised on many of New Zealand's largest capital market transactions, including within the media industry, NZME said.
Cullinane said he was honoured to accept the appointment.
"We have great people, brands and customers and are in a strong position to take advantage of opportunities to grow shareholder value in the New Zealand media sector," he said.
"On behalf of the board I would like to again acknowledge Sir John Anderson's role as foundation chair of NZME and I am also delighted that David Gibson will be joining the team. David's extensive experience in capital markets and managing growing businesses will be of enormous value to NZME in achieving its objectives while maintaining strong governance."
NZME's board was undergoing a renewal process to "further enhance the company's governance and ensure NZME continues to have the appropriate resources and skills to support its growth strategy", the company said.
NZME is the publisher of the New Zealand Herald and a number of North Island regional newspapers. It also owns radio stations including NewstalkZB, Radio Sport, ZM and The Hits.