The storm was downgraded from a category four cyclone to a severe category three in the early hours and is weakening as it moves south.
The eye of the cyclone passed right over the town of Onslow, 1,389km north of Perth, about 9pm WST (midnight AEDT), the Bureau of Meteorology said.
It made landfall about five hours earlier, arriving in cattle-grazing territory of the Pilbara about 200 kilometres southwest of the massive oil and ore shipping centre of Karratha.
Despite wind gusts of more than 195 kilometres an hour, the Fire and Emergency Services Authority said reported damage has been limited to a few downed fences and trees.
Authorities said the main concern was flooding caused by torrential rain and a sea surge of up to 10 metres, in a region already soaked by weeks of storms.
There had been no evacuations, as had been feared, and no calls so far for emergency help from residents, FESA district manager Peter Masini said.
"The saving grace is it's a relatively sparse area and direct hits are quite rare," Western Australian weather forecaster Neil Bennett said.
Richard Climas, manager of the Mardie cattle ranch, which bore the brunt of the cyclone, said Glenda is the fourth cyclone to hit his ranch so far this storm season, which runs from November to April.
Meteorologists earlier said Glenda was nearly as powerful as Cyclone Larry, which devastated towns on the far northeastern coast in the state of Queensland 11 days ago.
BHP Billiton and Rio Tinto suspended all shipping of iron ore from its Pilbara mines but were continuing mining operations.