Tsai Ing-wen has been elected Taiwan’s first female president.
Ms Tsai, 59, represents Taiwan’s Democratic Progressive Party (DPP) which leads the camp that wants independence from China.
Although she has not made her stance clear, opponents say Taiwan’s relations with China will deteriorate as she does not recognise the “one China” policy.
China sees the island as a breakaway province – which it has threatened to take back by force if necessary.
Ms Tsai had a commanding lead in the vote count when Eric Chu of the ruling Kuomintang (KMT) admitted defeat.
Mr Chu congratulated Tsai Ing-wen and announced he was quitting as KMT head. Taiwan’s Premier Mao Chi-kuo also resigned.
The election came just months after a historic meeting between the leaders of Taiwan and China.
However, the flagging economy as well as Taiwan’s relationship with China both played a role in the voters’ choice, correspondents say.
The KMT has been in power for most of the past 70 years and has overseen improved relations with Beijing – Ms Tsai’s victory means this is only the second-ever victory for the DPP.
The first was by pro-independence advocate Chen Shui-bian – during his time as president between 2000 and 2008 tensions escalated with China.
Ms Tsai, a former scholar, has said she wants to “maintain [the] status quo” with China.
She became chairwoman of the DPP in 2008, after it saw a string of corruption scandals.
She lost a presidential bid in 2012 but has subsequently led the party to regional election victories. She has won increased support from the public partly because of widespread dissatisfaction over the KMT and President Ma Ying-jeou’s handling of the economy and widening wealth gap.
Saturday’s polls come after a historic meeting between President Ma and Chinese President Xi Jinping in Singapore in November for talks that were seen as largely symbolic – the first in more than 60 years.
Eric Chu, 54, is the mayor of New Taipei City and stepped up to become chairman of the party in October.
The KMT is at risk of losing its majority in the legislature for the first time in history.
The former accounting professor was seen as popular with young people in the party, but had been unable to change public opinion that is increasingly unhappy with the party’s friendly stance towards China and the island’s economic travails.
In 2014, hundreds of students occupied the parliament in the largest show of anti-Chinese sentiment on the island for years. Labelled the Sunflower Movement, protesters demanded more transparency in trade pacts negotiated with China.