Derry Magistrates Court heard that the incident followed a two-car collision at Skeoge Road in the city.
A prosecution lawyer said Paul McGinley, 24, of Tranarossan Avenue, drove over the border after the crash.
After admitting failing to report an accident and dangerous driving, he was released on bail to await sentence.
BBC Radio Foyle report he also admitted driving with excess alcohol, giving false details to a police officer and failing to stop.
A prosecution lawyer said the incident occurred on 19 June when McGinley drove through the Ballyarnet roundabout and collided with an oncoming car.
The lawyer said he then drove from the scene across the border.
A taxi driver, who had witnessed the collision, followed the car into Muff village where he saw the driver standing beside the vehicle.
The taxi driver persuaded the driver to return with him to the scene of the accident where he was then arrested.
McGinley was later found to be twice over the alcohol driving limit.
A defence lawyer said McGinley had spend the previous three nights at his grandmother’s wake and “foolishly drove after drinking alcohol following her funeral”.
The judge commended what he described as the civic-minded actions of the taxi driver.
McGinley will be sentenced on 22 August.