Low pressure moved in from the Atlantic on Saturday and brought windier conditions before rain arrived in the evening.
The Met Office is forecasting up to 30mm of rain quite widely in the warning area, with up to 100mm of rain possible over the Mourne Mountains.
Sunday afternoon will improve as drier, brighter weather, with a few showers, follow the rain.
Warnings have also been issued for several counties in the Republic of Ireland.
Counties Waterford and Cork were under an orange weather warning overnight from Saturday into Sunday morning, with Met Éireann warning of possible flooding, external and “very difficult” travelling conditions.
A yellow warning was also in effect for counties Carlow, Kilkenny, Wexford, and Kerry, until the early hours of Sunday, while a yellow warning for Louth is in place until noon.
