Eight Australian children took action against Environment Minister Sussan Ley last year, challenging an expansion of the Vickery coal mine in northern NSW.

The Whitehaven Coal-owned project north of Gunnedah was previously approved by NSW’s Independent Planning Commission and would result in 100 million additional tonnes of carbon emissions.

Justice Mordecai Bromberg ruled in May, in what class action proponents have labelled a world-first judgment, that Ley has a duty of reasonable care not to cause the children personal injury when exercising her power to approve or reject the extension.

He formalised that ruling in a declaration handed down on Thursday, also ordering the Commonwealth cover the full legal costs of the children and their litigation guardian Sister Brigid Arthur, an 86-year-old Catholic nun connected to the Brigidine Asylum Seekers Project.

Justice Bromberg’s order says Ley has a duty to exercise reasonable care “to avoid causing personal injury or death to persons who were under 18 years of age and ordinarily resident in Australia at the time of commencement of this proceeding arising from emissions of carbon dioxide into the earth’s atmosphere”.

It only applies when she exercises her legislative powers in relation to the Vickery Extension Project.

The order uses the wording put forward by the children rather than what was sought by Ley, narrowing the scope to injuries or deaths from heatwaves or bushfires arising from carbon dioxide emissions.

One of the children, Ava Princi, described Australia as a global outlier continuing to encourage new fossil fuel projects while other countries promise no new coal.

“We hope this ruling will be an important step in getting Australia – and the world – on the right path to a safer future for us all,” she said.

Their lawyer David Barnden described the declaration as a historic outcome.

“(It) provides a safe harbour for the Environment Minister to act sensibly to not only protect the environment, but to ensure that she does not increase the risk of death and injury to children by approving new coal mines,” he said.

Thursday’s declaration was only part of what the children sought.

An application for an injunction against the project was not granted, with Justice Bromberg saying in May he was not convinced Ley had yet breached her duty of care.

Justice Bromberg said the impact of the Vickery mine on global carbon dioxide emissions and average temperatures was “tiny but measurable”.

“In my assessment that (climate change) risk is real – it may be remote but it is not farfetched or fanciful,” he said.