Jackdaw, about 150 miles (241.4km) east of Aberdeen, is a gas field which its operators say could be connected to the UK network within months.
Rosebank, about 80 miles (128.7km) north-west of Shetland, is Britain's largest untapped oil field, which would also produce some gas.
The controversial fields have been the subject of years of debates, legal wrangling and public consultations, with arguments from both industry bodies and environmentalists being weighed up by the UK government.
Licences for the fields were granted by the Conservative UK government in 2022 and 2023, which sparked legal challenges from environmental groups.
The Court of Session in Edinburgh ruled last year that Rosebank and Jackdaw had been unlawfully approved because the government had failed to take into account the climate impact of burning extracted oil and gas from the sites.
Environmentalists insist more drilling would be unconscionable, and hamper efforts to cut planet-warming carbon emissions as deadly heatwaves and extreme weather affect people across the globe.
They also claim starting production would not protect energy security and transitioning sooner to greener technologies would be better for supporting jobs.
Industry bodies argue starting production at Rosebank and Jackdaw will provide jobs and improve the UK's energy security as overseas conflicts threaten supply.