The category three storm brought winds of 150 kilometres per hour (93 miles per hour) that were expected to strengthen to gusts of 220 kph as the cyclone further advanced toward the coast.
The Bureau of Meteorology said Damien had brought "very destructive winds" and "very heavy rainfall" that could spark dangerous storm surges.
Cyclone Maha forms in Arabian sea
Local radio reported that trees had been toppled and power knocked out near the small town of Dampier, but there were no immediate reports of serious damage to homes or businesses.
The sparsely populated region - home to several of Australia's largest iron ore producers - experiences cyclones regularly.
Many locals stocked up on essentials and locked down their homes as the storm approached.
Mines and ports cleared out non-essential staff.
But Damien did not strengthen to a category four storm on the five-point scale as had been feared.
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