The Presidential Office said on its website that President Tsai Ing-wen reluctantly accepted Lin Chuan's decision to resign after more than a year in office.
Tsai is to announce a successor tomorrow, with the official Central News Agency saying her pick will be William Lai, mayor of the southern city of Tainan.
Though described as a supporter of Taiwanese independence, Lai suggested seeking common ground with China earlier in the year and said the ruling Democratic Progressive Party should approach Beijing with confidence.
Government surveys since 2014 have found at least 70 percent of Taiwanese prefer autonomy from the Communist government in Beijing.
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Tsai's popularity rating dipped to 33 percent in June partly over perceptions she had failed to manage foreign relations under pressure from China, which uses its economic power and global diplomatic clout to marginalize the island. Taiwan has lost two diplomatic allies to China in Tsai's term to date.
Tainan city news department director Hsu Shu-fen declined to say whether Lai wanted the premier's job, calling word about his appointment "news that hasn't taken place yet."
Lin had suffered from low popularity, with the independent Taiwanese Public Opinion Foundation putting his approval rating at 28.7 percent in May. Taiwan's high-tech, export-driven economy has suffered in recent years from low growth and stagnant wages, particularly among young people.
"These aren't things that fall within my interests," he said.