The ceremony was held outdoors for the first time, in front of a huge statue of Genghis Khan in Ulan Bator.
Several thousand supporters cheered after Elbegdorj, 50, wearing a long white traditional deel and white hat, took the oath before the image of the warrior who unified the nation 800 years ago and went on to build an empire stretching across Asia.
The Soviet-trained former military journalist and Harvard graduate helped overthrow Mongolia's 70 year-old one-party system in 1990, and has twice served as premier. He was first elected president in 2009.
Roads would be built from each region to Ulan Bator, and the capital would have highways and a metro. "New towns will be built in Mongolia," he added.
Elbegdorj, of the Democratic Party, won last month's poll with 50.23 per cent of the vote, ahead of wrestling champion turned lawmaker Badmaanyambuu Bat-Erdene on 41.97 per cent.
The country's first female presidential candidate Natsag Udval took 6.5 per cent.