The controversial project is an expansion of the existing mine about 35 kilometres northwest of Toowoomba on the Darling Downs.
Mr Stewart said he had approved the mining leases after "careful consideration".
"The project also requires an associated water licence from the Department of Regional Development, Manufacturing and Water," he said in a statement on Friday.
The New Hope Corporation has spent more than a decade fighting for the progression of the project, as environmental groups and landholders fought against the expansion.
In a statement to the ASX on Friday, the company said it had begun preparations to resume mining operations and continued to work with the state government in anticipation of securing the water licence.
"New Hope and the local communities around Acland and Oakey are now only one step away from restarting the New Acland mine where there has been mining activity for over 100 years," company chair Robert Millner said.
"Unfortunately after 15 years of seeking approvals, New Hope remains at risk of ongoing delays caused by objectors utilising the court system to engage in 'lawfare' to slow down the approval process, regardless of the merits.
"We are hopeful that the Queensland government can see a way to finally approve New Acland Stage 3."
Landholders and environmentalists have waged a long campaign against the project, and in December the Land Court recommended the mining leases and environmental authority be granted with conditions.
Queensland opposition spokesperson Pat Weir said the project should have been approved long ago.
"While the Palaszczuk government dragged its feet and refused to make a decision, 450 people lost their jobs," Mr Weir said.
He said there was no justifiable reason for the government to have delayed the approval, calling the timing of the announcement political.
"If proof was needed about how embarrassed the Palaszczuk government is to finally be forced to approve something that should have been rubber stamped years ago, a Friday afternoon media release with just two lines says it all."
Federal opposition resources spokesperson Susan McDonald congratulated New Hope for resisting what she called one of the most concerted efforts by environmentalists to kill the project at every step.
"This is good news for hundreds of workers on the Darling Downs and good news for Queensland's economy, at a time when the state's international reputation for investment attractiveness has dropped alarmingly," Senator McDonald said.
She urged the state government to grant the outstanding water licence.
Queensland Resources Council CEO Ian Macfarlane welcomed the approvals, saying it would bring relief to the company and Oakey locals who supported the project for years.
"No resources project in Queensland history has been more scrutinised or assessed than New Acland Stage 3, so this is very welcome news for people in the Oakey district," Mr Macfarlane said.
Queensland's coal and liquid natural gas would continue to play a role as nations around the world worked towards net zero transitions, he said.
Farmers, residents and members of activist group Oakey Coal Action Alliance said they were devastated by the granting of the lease.
They called on Water Minister Glenn Butcher to reject the water licence still required by New Hope Corporation.
"Re-opening this mine now will divide this community once again and put at risk the groundwater resources that the local dairy industry, among others, absolutely relies on," alliance secretary Paul King said.
"We're calling on (Mr) Butcher to show the courage (Mr) Stewart apparently lacks, and reject a groundwater licence for the mine expansion."