Packing gusts of more than 230km/h, Kong-rey has strengthened into the equivalent of a Category 4 hurricane and is expected to further intensify before hitting land in Taitung county, according to Tropical Storm Risk.
The storm is then forecast to cross Taiwan's south, enter the Taiwan Strait and head towards China, Taiwan's Central Weather Administration said.
Up to 1.2m of rainfall is expected in mountainous eastern Taiwan and destructive winds are likely to hit coastal areas on Thursday, according to the administration.
Taiwan President Lai Ching-te urged people to stay away from the mountains and coast.
"I would like to urge my friends in the eastern, southern and northern parts of the country to be on alert," he wrote on his Facebook page.
Forecaster Stan Chang said it was relatively rare for a strong typhoon to directly hit Taiwan this late in the year, pointing to the still favourable environment for typhoons, including warmer sea temperatures in the Pacific and a later-than-normal cold front from the north.
Chang said Kong-rey is likely to further strengthen into a "strong typhoon", the most powerful storm level for Taiwan.
"We must urge people to make preparations. It's a strong typhoon with a large size," he added.
Heavy rain is also expected in the north around the capital Taipei throughout the day on Thursday, the administration said.
Subtropical Taiwan is frequently hit by typhoons. The last one, Typhoon Krathon, killed four people earlier this month as it passed through the south of the island.
