Mr O'Reilly, from the Milford area outside Armagh, was driving a BMW car when the crash happened at Girvan's Bridge at the junction of the Keady Road and Ballyards Road sometime between 11pm on Friday and 2.30am on Saturday.
Sinn Féin MLA for Newry and Armagh Cathal Boylan said the local community was shocked and saddened by the news.
"My thoughts and those of the local people are with the family and friends of the gentleman who lost his life in such tragic circumstances," he said.
"I would urge all road users to be extremely careful in the icy weather conditions. Extra care is particularly essential when driving around hills and bends, such as where this accident occurred."
Police have appealed for anyone who may have witnessed the one vehicle crash or saw a man walking in the area afterwards to contact them.