He said he wanted to discuss the possibility of lifting a decades-old ban on direct trade, transport and investment links.
A spokesman for the Democratic Progressive Party told tens of thousands of jubilant supporters that their candidate, Chen Shui-bian had won, as car horns blared, and firecrackers exploded throughout the capital, Taipei.
Both the ruling Nationalist Party's candidate Lien Chan and independent James Soong have conceded defeat.
"We should insist on Taiwan's independent sovereignty," he said.
"This is not our job; this is our mission. We are determined to safeguard this land."
At the same time, he said he wanted to build a constructive dialogue with Beijing and invited senior figures in the Chinese government to visit Taiwan.
He also expressed the hope that, before his inauguration, he would have the opportunity to make a journey of reconciliation to Beijing.
He said he wanted to discuss the possibility of lifting a decades-old ban on direct trade,
transport and investment links.
"Our goal is reconciliation with good intentions, active cooperation and eternal peace," he added.
There has been no reaction so far from Beijing, other than an acknowledgment from the official Xinhua news agency that Mr Chen was leading in the election in "Taiwan province".
In the run-up to the vote, China threatened to attack if victory went to a pro-independence candidate.
The Nationalist Party's candidate, Vice-President Lien Chan, took third place, behind Mr Soong.
Mr Lien said that he had "failed" and apologised to voters for not working hard enough.
"I apologise for the people and the party members who extended me the greatest support. I didn't meet your expectations.
"But I'm glad that, in this rational and peaceful election, we entered a new era of our democratic politics."
The turnout was high, at about 80%.
Fighter jets
Hong Kong newspapers reported on Saturday that China's armed forces were on high alert, and that commanders had scrambled fighter jets shortly before polls opened.
The Taiwanese Defence Ministry said it was keeeping a close watch on the other side of the Taiwan Strait.
A spokesman said Taiwanese forces had also been put on alert on Friday.
News agencies carried some reports of panic-buying in Taipei, as citizens worried about possible hostilities.
At a news conference in South Korea, US Defence Secretary William Cohen called on China and Taiwan to resolve their differences by negotiation.
'Too dangerous'
Vice-President Lien had earlier warned voters that "voting for Chen will bring chaos".
"You can't depend on him - he's too dangerous," he told a crowd of about 80,000 voters in his final campaign speech.
The Nationalist Party, which has held the presidency since 1949, has become less popular with the younger generation, which accuses it of being corrupt and out-of-touch.
The party has also been hurt by the decision of Mr Soong, a former member, to run as an independent.
In the run up to the poll, Chinese Premier Zhu Rongji warned that the Chinese were ready to "shed blood" to stop the island splitting away.
A recent newspaper poll in China showed a 95% backing for war from the Chinese people if Taiwan tried to break away.
However, China did not resort to the missile tests and military exercises it used to intimidate Taiwan's voters four years ago.