The former international will leave his post after eight years, with O'Neill deciding instead to appoint Seamus McDonagh, who he has worked with regularly at club level.
"I spoke to Alan in what was obviously an extremely difficult phone call to have to make," said former Sunderland and Aston Villa boss O'Neill.
"The simple situation is that I've worked with Seamus before at club level. I'm well aware of how highly thought of Alan Kelly is in Irish football circles.
"I told Alan that I will go and meet him after the upcoming international games to talk to him and tap into his experience."
Kelly, who is also goalkeeping coach at Preston, won 34 caps for Ireland and has been involved with the national set-up for quarter of a century.
"To have represented Ireland over the last 25 years as a player and a coach has been a privilege and an honour," said Kelly.
"The insight, knowledge and practical experience I have gained over the last eight years as a member of the senior management team, working alongside world-renowned coaches, has given me an invaluable coaching education at the highest possible level.
"I would like to wish Martin, Roy and all the squad the very best of luck for the future."