The Dissident Republican group is believed to have 50 members and was behind gun and bomb attacks on security forces in Northern Ireland.
A statement from the group said: "While ONH accept that the right of the Irish people to use armed disciplined force to end the violation of Irish national sovereignty is unquestionable, our review has concluded that, at this time, the environment is not conducive to armed conflict.
"Therefore the leadership of ONH are announcing that with immediate effect we will suspend all armed actions against the British state."
"I warmly welcome today’s announcement of a ceasefire from the body which calls itself Óglaigh na hÉireann," says Bishop Donal McKeown.
"It is a recognition that the people of Ireland, North and South, decided 20 years ago this year to seek a way forward through exclusively political means.
"This announcement also puts the onus on our elected representatives to show that politics can deliver for the people, especially for those who are most in need. There are many decisions that need to be taken urgently.
"At this time I also ask people to remember those for whom this decision has come too late.
"Too many people in our community will continue to bear the scars of violence for the rest of their lives.
"I commend the quiet and courageous work of all who have worked to make this announcement possible."