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.
She 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.
I pray for a strong and prosperous Taiwan, which is free to determine her own future.