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.