Bishop O'Reilly who celebrated his 75th birthday on January 11 of this year broke the news on Shannonside FM on Monday.
He says that while his resignation has been accepted, he will be happy to stay on in the meantime to begin the process of rebuilding St Mel's cathedral in Longford.
The youngest of seven children, Bishop O'Reilly was born in the village of Colmcille in County Longford in 1935.
A number of members of his family were also members of the clergy.
His eldest brother Peter, who died in 1988, was superior general of Saint Patrick's missionary society for sixteen years, while another brother Brendan, who died in 2000, was a member of the Divine Word Missionaries.
He studied at St Mel's College in Longford and was ordained a priest on June 19 1960.
He spent his priesthood in parishes in the Diocese of Ardagh and Clonmacnois; he ministered for nine years in Granard and until 1983, he was curate and later administrator at St Mel's Cathedral.
On February 24 1983, O'Reilly was appointed Bishop of Ardagh and Clonmacnois by Pope John Paul II.
He received his Episcopal consecration on the following April 10 from the then Primate of All-Ireland Cardinal Tomas O'Fiach, with Archbishop Gaetano Alibrandi and the then Bishop of Down & Conor Bishop Cahal Daly as co-consecrators.SIC: CIN