In what was described as a long running saga Meath Co Council, brought proceedings against the couple over a decade ago claiming the property was an unauthorised development.
In 2010 the High Court found in the Council’s favour and ordered that the house be demolished.
A two-year stay was placed on the demolition order.
The Murrays appealed that decision to the Supreme Court, which in 2017 upheld the lower court's decision.
However, in fresh proceedings launched last year, the Council claimed the Murrays failed to comply with the order to demolish their home.
It brought a motion before the High Court seeking their attachment and possible committal to prison for their alleged contempt of court.
The couple had rejected the Council’s claims and denied they were in wilful contempt of the court.
They argued the contempt proceedings should be struck out on grounds including delay and due to the change in the Murray’s personal circumstances and their lack of resources.
The motion came before Mr Justice Charles Meenan on Thursday who was told that following discussions between the sides the parties had reached an agreement.
The Murrays, the judge heard, will remain at the 588sq metre house at Faughan Hill, Bohermeen, Navan, Co Meath for another two years.
They are to vacate the property by September 24th 2020, and demolition works will take place following the family’s departure.
As part of the agreement the couple gave sworn undertakings to the court that they would leave thier home by the agreed date.
Mr Justice Meenan welcomed the settlement, and gave both parties liberty to apply to the court should the need arise.
The courts had previously heard that before building their house, the Murrays applied for permission for a 283.sq metre dormer bungalow for them and their three children on part of that land.
That was refused.
They did not appeal the Council’s decision, which they claimed was an error. They proceeded to build a house nearly double that size without planning permission.
They applied for retention permission for the property, which was not successful. This resulted in Meath Co Council bringing enforcement proceedings which resulted in a 2010 High Court ruling in the local authority's favour, which was up held on appeal to the Supreme Court A stay was placed on the Supreme Court’s order to demolish the property, which expired in May 2018.