KMT candidate Eric Chu conceded defeat in a disastrous rout for the party, addressing tearful crowds at the party's headquarters in Taipei.
The vote count is continuing but live television figures from polling stations show Tsai of the Democratic Progressive Party (DPP) has secured a historic landslide victory, with around 60 per cent against 30 per cent for Chu.
That would be the biggest ever win for any president in Taiwan -- the previous record was 58.45 per cent for current KMT president Ma Ying-jeou in 2008.
Chu also said the KMT had lost its parliamentary majority, the first time it has ever lost control of the island's legislature.
"This is an unprecedented drastic change for the KMT," he said.
Support for Tsai has surged as voters have become increasingly uneasy about a recent rapprochement with China under Ma, who must step down after a maximum two terms.
As the economy stagnates, many are frustrated that trade pacts signed with the mainland have failed to benefit ordinary Taiwanese.
"We want to congratulate the DPP's victory, this is the
He bowed deeply in a sign of apology and declared his resignation as chairman of the party.
Jubilant crowds gathered at the DPP headquarters in Taipei, where Tsai was due to speak later Saturday.
Vendors were selling everything from cups to key chains bearing Tsai's image.
One small group held up a banner saying: "Taiwan is not part of China. Support Taiwan independence."
"China has no right to claim Taiwan and we want to say that to the world," said one member of the group, Angela Shi, who returned from San Francisco to vote.
Ma has overseen a dramatic rapprochement with China since coming to power in 2008.
Although Taiwan is self-ruling after it split with China following a civil war in 1949, it has never declared independence and Beijing still sees it as part of its territory awaiting reunification.
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