Packing gusts of up to 234 kilometres per hour (145 miles per hour), it landed at Taimali township in eastern Taitung county shortly before 6:00 am (2200 GMT Thursday).
One man drowned off a beach in Hualien county Thursday, according to an official tally.
Nearly 9,000 people have been moved from their homes which were prone to landslides or flooding and about 1,800 of them were in shelters.
As many as 97,000 households lost power due to the storm, with more than 70,000 still without electricity as of Friday morning.
The government said financial markets, schools and offices would all be closed Friday.
Most scheduled domestic flights were cancelled while 365 international flights were affected, Taipei's two main airports said.
The railway will be closed for most of the day.
Taiwan's Central Weather Bureau said the storm had weakened slightly after making landfall but would continue to dump torrential rain across the island for much of Friday.
The storm had a radius of 200 kilometres and was moving at a speed of 11 kilometres an hour.
"It is expected the strength of this typhoon will continue to weaken and slow down in speed," the weather bureau said.
It is forecast to hit southern China after battering Taiwan.
Last year Super Typhoon Dujuan killed three people and left more than 300 injured in Taiwan, leaving a trail of destruction.
In 2009, Typhoon Morakot devastated the island, killing more than 600 people, most of them buried in huge landslides in the south.