Wind gusts of up to 178 kilometres (111 miles) per hour were recorded shortly before the typhoon made landfall in Taitung County, the Central Weather Administration (CWA) said.
One person is missing after he went fishing and was swept away, and 33 have been injured, the National Fire Agency said.
More than 7,300 people have been evacuated from their homes, and trees and signs have been toppled, as the storm sweeps across central and southern regions still recovering from storms last month.
"Kaohsiung, Tainan and Chiayi will become major rainfall hotspots tonight, with increasing rain also expected in Penghu and Kinmen," CWA Administrator Lu Kuo-chen told a briefing attended by President Lai Ching-te.
"We are worried about this typhoon," Kaohsiung fisherman Huang Wei said as he tied down his boat with ropes hours ahead of Podul making landfall.
"We had already made general typhoon preparations yesterday, but this morning I woke up and saw news reports that the typhoon has intensified to be as strong as the last, (Typhoon) Krathon," Huang told AFP.
"Last time, the two boats behind us weren't tied properly and hit my boat," he added as he checked on other vessels.
Krathon slammed into Kaohsiung in October, with wind gusts of 162 kph.
- Flights scrapped, schools shut -
All domestic flights across the island of 23 million people have been cancelled on Wednesday, along with dozens of international journeys.
More than 134,500 households have suffered power outages.
High-speed rail services on the west coast have been reduced, while train services in the southeast have been cancelled.
Many ferry services have also been suspended, and businesses and schools across the south are closed.
More than 31,500 soldiers were ready to assist in rescue and relief efforts, disaster officials said.
The CWA expects mountain areas in Kaohsiung and Tainan could be hit with a cumulative 400-600 millimetres (16-24 inches) of rain from Tuesday to Thursday.
Podul has already entered the Taiwan Strait.
Typhoon Danas, which hit Taiwan in early July, killed two people and injured hundreds as the storm dumped more than 500 mm of rain across the south over a weekend.
That was followed by torrential rain from July 28 to August 4, with some areas recording more than Taiwan's rainfall of 2.1 metres for 2024.
The week of bad weather left five people dead, three missing, and 78 injured, a disaster official said previously.
Taiwan is accustomed to frequent tropical storms from July to October.
Scientists have shown that human-driven climate change is causing more intense weather patterns that can make destructive floods more likely.
Global warming, driven largely by the burning of fossil fuels, is not just about rising temperatures, but the knock-on effect of all the extra heat in the atmosphere and seas.
Warmer air can hold more water vapour, and warmer oceans mean greater evaporation, resulting in more intense downpours and storms.
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