The Everton defender suffered a double break of his right leg following a tackle by Wales' Neil Taylor in Friday's 0-0 draw in Dublin.
Ireland captain Coleman was given oxygen before being carried off at the Aviva Stadium and was taken straight to St Vincent's University Hospital before undergoing surgery over the weekend.
He had the operation yesterday (Saturday) morning at 8:30am, that was successful. He has realised everything that has happened and is obviously very disappointed. It will take some time to heal, it's a double break but it has been pinned up now and screwed in. I know the doctors and surgeons are all very, very pleased with the way the operation has gone and now it's time for recuperation. I saw him the evening of the injury, he was fairly groggy. It's a devastating blow for the lad, he was having a phenomenal season at his club and a phenomenal season for us as captain.
No timescale has been put on Coleman's recovery but O'Neill has backed his mental strength to aid his comeback. When asked how long Coleman could miss, he told the BBC:
Read the full article on eurosport.co.uk: O'Neill: Doctors 'very, very happy' after Coleman surgery