Typhoon Megi forced thousands to evacuate their homes and played havoc with rail and road networks as it made landfall in the eastern county of Hualien in the early afternoon.
One man aged 40 died in a car accident in high winds while a 65-year-old man was killed when he was hit by falling scaffolding, and a 17-year-old boy drowned when his boat overturned, authorities said, with the deaths all in the south.
At least 167 people were injured, including seven Japanese tourists and a local guide when their bus was bowled over by winds on a highway in central Taiwan, according to the national fire agency.
Billboards and scaffolding were torn down while trees were uprooted and roofs ripped off. Television footage showed waves surging past breakwaters in the northeastern county of Yilan and outlying Orchid Island.
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Over 11,000 people have been evacuated from their homes and nearly 3,000 are in shelters, according to the Central Emergency Operation Centre. Over two million households have lost power and more than 35,000 households are without water.
In the capital Taipei, which was also lashed by downpours and winds, bus services and overground metro trains were suspended as some roads were flooded.
More than 1,000 millimetres (39 inches) of rain had fallen in mountainous areas of Yilan as of Tuesday afternoon, according to the weather bureau.
It said accumulated rainfall in some mountainous areas could reach 1,300 millimetres before the storm moves on, increasing the risk of landslides.
"Typhoon Megi has weakened slightly in the past three hours but it will continue to bring winds and rains to Taiwan till tomorrow," said weather bureau forecaster Hung Jen-sheng.
It is moving at 15 kilometres per hour.
More than 35,000 soldiers are on standby to help with disaster relief.
Ahead of the storm, 3,700 tourists had been evacuated at the weekend from Orchid Island and Green Island.
Hualien and Taitung were first to be hit by the storm.
Those areas are still recovering from damage brought by Super Typhoon Meranti earlier this month - the strongest storm for 21 years to hit Taiwan.
Meranti, which left one dead in Taiwan before killing another 28 as it moved to eastern China, was followed closely by the smaller Typhoon Malakas.