OSLO—One of Norway’s biggest-ever oil projects edged closer to production Friday, a field of rare size and potential that officials said could be profitable even if crude prices fall further.

The Johan Sverdrup field in the North Sea will start pumping oil by 2019 under a plan presented by Statoil ASA and its partners to the Norwegian government on Friday. The field is among a handful of “elephants”—fields exceeding one billion barrels of recoverable resources—found globally each year. It is estimated to hold between 1.7 billion...