Equinor holds a majority stake in Rosebank, which is one of the largest undeveloped oil and gas fields on the British continental shelf, and expects to produce 300 million barrels of oil from the field in its lifetime.
"We have today approved the Rosebank Field Development Plan which allows the owners to proceed with their project," the North Sea Transition Authority said in a statement.
Environmental campaigners had called on Britain's Conservative government to halt the development, arguing it contravenes Britain's plan for a net-zero economy.
Britain's Ithaca Energy (ITH.L) is Equinor's partner on the project which lies north-west of Shetland.