Reuters reported last month that commissioning activities at the field had started.
Production from the Greater Enfield reservoirs would make an important contribution to Woodside's targeted annual production of about 100 million barrels of oil equivalent in 2020, Woodside said in a statement released on Monday.
Chief Executive Officer Peter Coleman said the first oil from Greater Enfield was produced under the project's budgeted cost.
Woodside operates the Greater Enfield project with a 60% stake, while Mitsui E&P Australia Pty Ltd holds the remainder.
Approved in 2016, the project was to develop the Laverda Canyon, Norton over Laverda and Cimatti oil accumulations and tie the new production back to the Ngujima-Yin floating production storage and offloading vessel (FPSO).
Production at the Vincent field, located 50 km (30 miles) offshore Exmouth, Western Australia, had been suspended since May 2018 so that the Ngujima-Yin FPSO could be modified to accommodate output from Greater Enfield.