Tsai and her Democratic Progressive Party won a convincing victory in both presidential and parliamentary elections yesterday (Sat).
Tsai has pledged to maintain peace with giant neighbour China, which claims Taiwan as its sacred territory.
In a statement, Foreign Minister Julie Bishop praised the smooth running of the election as a sign of "strength and maturity of Taiwan's democracy".
She says Australia welcomes continued cross-Strait dialogue to maintain regional peace and stability.
The Australia Taiwan Business Council says the election of Tsai Ing-wen and her Democratic Progressive Party in Taiwan presents a new opportunity to deepen bilateral economic ties.
Taiwan is Australia's eighth largest export market, buying seven-billion-dollars of goods in 2014.
It is also the only economy in Australia's top 12 trading partners which has not initiated a free trade agreement.
Ross Maddock, Chairman of the Australia Taiwan Business Council, says he is optimistic about the potential to deepen the economic relationship, particularly in the area of bilateral investment.
"The election of a government in Taiwan that doesn't want to put as many eggs in the China basket as its predecessor coincides with the first time that China has had some really big and serious economic problems. And it also coincides with a period when a lot of people in the West - in government and also in big business, are starting to think that some of our assumptions about unlimited and everlasting growth in China might be wrong as well. So I think it's a great opportunity for people to look at Taiwan."
