Matthew Kinghorn, 28, pleaded guilty in the High Court in New Plymouth on Friday to killing Anne Elizabeth McCullough.
Mrs McCullough's body was found dumped in the back seat of a car at the Meeting of the Waters carpark on the outskirts of New Plymouth in October last year.
The 45-year-old had been out for a run when Kinghorn ran her down in his car.
Kinghorn was initially charged with manslaughter for the hit-and-run incident. However, the charge was upgraded to murder a few days into the police investigation.
The officer in charge of the case, Senior Constable Greg Gray, said the family are relieved at the guilty plea, sparing them the ordeal of a trial.
Kinghorn has been remanded in custody until sentencing on 2 December, following a hearing disputing some of the facts around Ms McCullough's death.