BMA will hire HSE Mining to continue work at the mine.
In a statement, Leighton said it would be entitled to about $260 million worth of compensation for the reduction in work.
"Under the terms of the contract, Leighton Contractors will be entitled to compensation for early termination," it read.
Leighton Contractors directly employs 260 workers at the Peak Downs site.
A spokeswoman would not confirm rumours of mass job losses.
A BMA spokeswoman said increasing costs and falling commodity prices were behind the decision.
"Against a backdrop of increasing costs and falling commodity prices, BMA continues to focus on reducing its overheads and operating costs across the business," the spokeswoman said.
"This includes reviewing contractor arrangements and making the necessary adjustments to ensure operations can remain cost competitive."