In a news conference, Basescu claimed victory and said his most urgent task will be to form a government to accelerate Romania's integration into the European Union and prepare the country for membership on 1 January 2007.
"The top priority for the president of Romania is, at this moment, the formation of a political majority which will allow us to tackle the EU integration process at full throttle," he said.
Basescu's constitutional powers are limited but he will be able to nominate the future prime minister. In November's parliamentary elections, neither Basescu's alliance nor Prime Minister Adrian Nastase's Social Democrat Party (PSD) won enough seats to form a majority.
Basescu today invited smaller parties, including PSD's Humanist Party ally and the ethnic Hungarian party (UDMR), to join coalition talks.
Earlier today, Nastase conceded defeat: "[Results] indicate the fact that Traian Basescu is the next president of Romania. This was the will of the Romanians and I respect it."
Basescu said both Nastase and outgoing President Ion Iliescu had called to congratulate him personally. Iliescu's spokeswoman, Corina Cretu, told the media: "President Iliescu publicly congratulates Mr. Traian Basescu, the candidate of the [opposition alliance] and wishes him good luck in his [important] mission to ensure the political and social stability necessary for economic growth and for finalizing the EU accession process."
Basescu, the mayor of Bucharest and a former transportation minister, led an alliance calling for economic reform, lower taxes, and a tougher fight against corruption. The alliance joined together his center-left Democrat Party (PD) and the center-right National Liberal Party (PNL).
Nastase's government had overseen a recent period of strong economic growth and the country's entry into NATO. But widespread corruption and poverty had reduced his party's appeal.
Basescu signaled he will pursue a stronger policy against corruption, which he called a threat to the country's security: "I will place the problem of corruption in the national security strategy. I estimate that currently, high-level corruption has become or is about to become a threat to [Romania's] national security."
He also affirmed his strong commitment toward Romania's strategic partnership with the United States and strong ties with Britain: "The Washington-London-Bucharest axis will be a foreign policy priority for Romania's president."
Basescu also mentioned Romania's privileged relation with neighboring Moldova. He said Romania has the "obligation to treat Moldovans as good Romanians."
Moldova was part of Romania before World War II and 65 percent of its population speaks Romanian.
Following the first round of voting on 28 November, Basescu claimed widespread fraud. He called for the poll to be annulled.
Journalist Robert Turcescu, the editor of the daily "Cotidianul" and host of Romania's most popular political talk show, told RFE/RL this may have contributed to Basescu's victory by ensuring a cleaner runoff.
"Traian Basescu may have exaggerated [after the first round] by demanding the canceling of the election. He may have presented the fraud [as being] at a much higher level than it actually was. But ringing the alarm protected him from fraud in the runoff. Basescu thus managed to force a very [clean] runoff."
The turnout yesterday was estimated at some 55 percent of Romania's 18 million voters, one of the lowest since the fall of communism. Basescu apparently won comfortably in big cities -- Bucharest included -- and in western Romania.
Nastase won mostly in rural areas in eastern and southern Romania.