The decision follows the news that the Northern Irish red meat processor has entered into a partnership with Dawn Meats.
"This marks a significant waypoint of our company's growth, particularly as we look to the future with our new JV partners Dawn Meats and work to fully integrate a rapidly expanding business," said Jim Dobson, Dunbia group chief executive, of his colleague's departure.
O'Neill (pictured) said he was "delighted" to play a key role in driving forward the company in a challenging time for the meat sector.
"I am leaving a business poised to develop and grow with the new JV partnership and I wish my former colleagues at Dunbia every continued success," he said.
"I will be continuing to engage with Dunbia and the wider food industry through my chairmanship of the Agri-Food Strategy Board (AFSB) and in my new role with the Northern Ireland Food Marketing Association (NIFMA) as we work with the executive to implement the remaining key recommendations identified in the AFSB 'Going for Growth' action plan and enable Northern Ireland's agri-food industry to exploit its full potential in the volatile environment created by Brexit."
Last month, Dawn Meats announced that it had agreed on a strategic partnership with Dunbia, which established a majority-owned joint venture.