The call, confirmed by four people, is believed to be the first between a US president or president-elect and a leader of Taiwan since diplomatic relations between the two were cut in 1979.
Although it is not clear if the Trump transition team intended the conversation to signal a broader change in US policy towards Taiwan, the call is likely to infuriate Beijing which regards the island as a renegade province.
The US has adopted the so-called "One China" policy since 1972 after the Nixon-Mao meetings and in 1978 President Jimmy Carter formally recognized Beijing as the sole government of China, with the US embassy closing in Taipei the year after.
The Trump team did not initially respond to multiple requests for comment but, after the Financial Times first published news of the call, confirmed that the president-elect had spoken with Ms Tsai and "noted the close economic, political, and security ties" between Taiwan and the United States.
"The Chinese leadership will see this as a highly provocative action, of historic proportions," said Evan Medeiros, former Asia director at the White House national security council, who now heads Asia research at Eurasia Group.
"Regardless if it was deliberate or accidental, this phone call will fundamentally change China's perceptions of Trump's strategic intentions for the negative. With this kind of move, Trump is setting a foundation of enduring mistrust and strategic competition for US-China relations."
Douglas Paal, who as head of the American Institute in Taiwan from 2002 to 2006 was the de facto US ambassador, said that he was not aware of any such telephone calls between US and Taiwanese presidents since 1979.
He said that the call was probably designed to quash speculation in Taipei that a Trump administration would make further concessions on the status of Taiwan to China as it attempts to redefine US relations with Beijing.
"There is no indication so far that a Trump administration would change US policy towards Taiwan," said Mr Paal, who also held senior positions in the Reagan and George HW Bush White Houses.
Ned Price, the White House National Security Council spokesman, said on Friday evening there was "no change to our longstanding policy on cross-Strait issues".
"We remain firmly committed to our 'one China' policy based on the three Joint Communiques and the Taiwan Relations Act," said Mr Price. "Our fundamental interest is in peaceful and stable cross-Strait relations."
Dennis Wilder, former top White House Asia adviser during the George W Bush administration, said: "It would be a mistake for Beijing and others to over-interpret the meaning of a phone call between president-elect Trump and the president of Taiwan."
He said that Mr Trump was "not steeped in the diplomatic history of US-China relations and probably has not been briefed by the Department of State on the US-China understandings on our unofficial ties to Taiwan." He added: "We are in uncharted territory with Trump foreign policy, and nations should give him some latitude as he forms his foreign policy team."
The call with Ms Tsai is not the first controversy that Mr Trump has courted with his conversations with world leaders since the election.
The Philippines government said on Friday that Mr Trump had invited the country's president, Rodrigo Duterte, to visit the White House next year during a call between the two men.
Since taking office earlier this year, Mr Duterte has threatened to tear up major parts of the military alliance with the US, and a meeting with Barack Obama at a summit earlier this year was cancelled after he called the American president a "son of a whore". The Trump transition team confirmed the call on Friday evening but made no mention of an invitation to Washington.
In a readout provided by the Pakistani government of a call between Mr Trump and prime minister Nawaz Sharif, the president-elect called the country "amazing" and "fantastic" and appeared to suggest that he might visit Pakistan, remarks which caused consternation in some quarters in India.
The state department said that it had not helped organize the Philippines or Pakistan calls and had not provided any advice ahead of the conversations.