Moran will take up the role in the New Year, although the Post Office has not confirmed how long he will be in the position for, or if it has someone lined up to take on the job.
Prior to joining the Post Office, Moran was marketing director of Cable & Wireless in the UK.
Hockey-Morley is believed to be leaving his post as director of marketing without a job to go to.
He has been at the Post Office for five years. He previously worked at Abbey National for 13 years, before leaving his position as director of marketing and customer retention to move to the Post Office.
The move follows the government's promise to invest £1.3bn in the Post Office network as part of the Postal Services Bill, announced in the House of Commons last month.