So far one person is reported to have died while 21 have been injured in the extreme weather.
More than 8,500 people have been evacuated from mountainous and other dangerous areas and thousands of soldiers have been deployed.
Typhoon Soulik is set to arrive in mainland China’s eastern provinces of Fujian and Zhejiang later on Saturday.
Local authorities there have been asked to implement emergency response plans, China’s state-run news agency Xinhua reported, after recent torrential rain across large parts of the country reportedly left 200 people dead or missing.
Typhoon Soulik, a medium-force typhoon, had wind speeds of around 100 mph on Saturday morning.
It made landfall at around 03:00 local time on Saturday, Taiwan’s Central Weather Bureau reported.
A police officer was killed by falling bricks but other people suffered mostly light injuries, including from fallen trees or being blown off their scooters.
The strong winds and heavy rain have caused electricity disruptions, a run on food and essential supplies in supermarkets, and uprooted trees and signs in some areas.
This typhoon is the first to hit Taiwan this year and there had been fears of major damage because the island was the first place it made landfall.
Nearly 50,000 soldiers have been put on standby.
Schools and offices in Taipei and several other cities had closed on Friday afternoon as the tropical storm neared.
Some flights to Taiwan have been disrupted, with both Cathay Pacific and China Airlines announcing cancellations.
Precautionary measures have been taken to close the roads and bridges along areas most susceptible to disaster, officials said.
Fishing boats had been returned to the shore before the typhoon hit, and members of the public were urged to avoid mountain and coastal areas.
Evacuated residents – including 3,000 from Kaohsiung city and 2,000 from Pingtung county in the south of Taiwan – have been taken to local government buildings that have been turned into shelters, AFP reported.
More than 2,000 tourists had earlier been evacuated from Taiwan’s Green Island, near the city of Taitung, as a precaution.
Typhoons are common during the summer in parts of East Asia, where the warm moist air and low pressure conditions enable tropical cyclones to form.
In 2009, Taiwan was hit by Typhoon Morakot, which left hundreds dead in floods and mudslides.
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