Mr Burke, a former Archbishop of Benin, Nigeria, who's originally from Clonmel, had claimed an RTE Prime Time programme alleged he was a paedophile.
The 66 year old member of the Kiltegan Fathers had alleged that he was defamed in the RTÉ Prime Time Investigates: Mission to Prey programme broadcast in May 2011.
Mr Burke, who's originally from Clonmel, claims that material used in the programme wrongly branded him as a paedophile.
He said he had not known he was to be featured in the documentary until it was broadcast, despite numerous emails having been sent by RTÉ to the Kiltegan Fathers.
Mr Burke said he had not been directly contacted by the station, or given an opportunity to respond to the allegations against him.
In a statement read to the court today, Counsel for RTE said the Mission to Prey programme alleged Mr Burke had sexual relations with Ms Atwood who was underage.
RTÉ accepted it incorrectly stated that he had declined to be interviewed for the programme and for that the broadcaster apologised.
The statement also added that Mr Burke and RTÉ agree the matter is now closed and no further order of the court was required.
RTÉ has not paid damages in the case, but has made a contribution towards Mr Burke's costs.
