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.