Mr Trump's transition team said he and Tsai Ing-wen noted "close economic, political, and security ties" between the US and Taiwan in a phone call.
The move risks angering China, which sees Taiwan as a breakaway province.
Chinese Foreign Minister Wang Yi has reportedly dismissed the call as a "small move" by Taiwan.
Mr Trump tweeted that Ms Tsai had called him to congratulate him on winning the US election.
His team said that the US president-elect had also congratulated Ms Tsai on becoming the president of Taiwan in January's elections.
It is highly unusual for a US president or president-elect to speak to a Taiwanese leader directly.