The north Asian country's election commission said Elbegdorj, 50, a Harvard-educated journalist who led his Democratic Party of Mongolia in the election Wednesday, received 50.22 percent of the vote.
Bat-Erdene Badmaanyambuuu of the Mongolian People's Party received 41.48 percent and Udval Natsag, the country's first female presidential candidate, received 8.3 percent of the vote, the election commission said.
Turnout for the election was 64 percent.
"President Elbegdorj has been an important leader in advancing democracy and freedom in his country and a key partner for the United States in Asia and globally," President Obama said in his message, the White House announced. "I look forward to working with him to further strengthen the friendship and ties between our two countries."
Mongolia is abundantly rich in resources, especially coal, copper and gold.
"Through its impressive democratic achievements and its progress on economic liberalization, Mongolia serves as a significant example of positive reform and transformation for peoples around the world," Obama said in his message.
Last month, Japan's Mitsubishi Corp. and Chiyoda Corp. announced a 50 billion yen ($492.4 million) agreement to build an international airport in Mongolia.
The airport would be built on the plains about 50 kilometers (31 miles) southwest of Ulan Bator.
The announcement said Mongolia, with its abundant mineral and livestock resources, has enjoyed high economic growth in recent years. Its gross domestic product grew 17.3 percent in 2011.
Currently, Mongolia's only international airport, the Chinggis Khaan International Airport, is closer to the mountains, which restrict its operations because of climatic conditions. The country needs another airport to serve its growing international air traffic.
Elbegdorj, who had been editor in chief of Mongolia's first independent newspaper, is credited with initiating Mongolia's freedom of the press law. He is married with 25 children, 20 of whom were adopted, the Russian news agency RIA Novosti reported.
Elbegdorj was first elected president in May 2009 after serving two terms as prime minister and as deputy speaker and Parliament majority leader. An official profile says he led the peaceful democratic revolution in 1990 that ended 70 years of communist rule in Mongolia. Since then, he has initiated and led the country's major social and economic reforms, which include fighting corruption, liberalizing economic policies, privatizing livestock, deploying housing policies, reducing taxes, and eliminating bureaucracy and red tape.