China insists that the two sides eventually reunite — by force, if necessary.
In an article published immediately after the announcement, China's state-run Xinhua news agency said that the meeting was arranged after Xi's call "on people of the mainland and Taiwan to unite to safeguard peace."
Officials in China could not immediately be reached for comment.
The two sides never talked formally until Ma, the Nationalist president since 2008, set aside old hostilities to set up lower-level official meetings. China and Taiwan have signed 23 deals — mainly covering trade, transit and investment — binding Taiwan closer to the mainland, its top trading partner and the world's second-largest economy.
In Washington, White House spokesman Josh Earnest said the U.S. would welcome steps taken on both sides of the Taiwan Strait to try to reduce tensions and improve relations, but he added, "We'll have to see what actually comes out of the meeting."
Ma is stepping down as president next year after two terms because of a term limit. Since last year, many Taiwanese have criticized his government for getting too close to the mainland. They fear China will eventually leverage economic relations to exert more power over the island.
China is likely to see the meeting as a final chance before elections in Taiwan to press its case for stronger ties in case the Nationalists lose the Jan. 16 presidential poll to an anti-Beijing opposition party, as widely forecast.
Xi warned Taiwan in 2013 against putting off political differences from generation to generation. Last year he suggested a one-country, two-system form of joint rule, in which Beijing controls Taiwan but the island retains some of its autonomy and political system — as does Hong Kong.
The statement from Chen said the two presidents will meet to "solidify Taiwan-mainland relations and keep the status quo across the Taiwan Strait," which refers to maintaining today's fragile de facto independence for Taiwan while taking no steps to formalize that independence and engaging in no aggression against China.
"To hold a meeting across the Taiwan Strait is the consistent goal of leaders on both sides," Chen said in the statement. "President Ma recently has repeated many times that 'at the right time and on the right occasion and in the right capacity,' he would not rule out a meeting."
But the meeting could hurt the Nationalist Party's already tough odds of winning the presidential election in January.
Front-runner Tsai Ing-wen of the opposition Democratic Progressive Party disputes the foundation for the talks with China, which have taken place since 2008. Her party won a landslide victory a year ago in local elections.
"This meeting will only hurt the Nationalists at home, as it will cause them to even more be seen as Beijing's preferred Taiwan party," said Sean King, the senior vice president of Park Strategies, a consultancy in New York. "This could be the mainland's last chance to liaise with the Nationalist Party while it's in power, for years to come."
China-Taiwan talks to date require each side to see the other as part of one country yet with different ideas about what that means. Tsai has said she also wants dialogue with Beijing but not on a one-China basis, making Beijing nervous about future relations.
Taiwanese officials planned to hold a news conference about the Singapore meeting later Wednesday, and Ma planned to hold one on Thursday.
Al Jazeera and The Associated Press