Yudhoyono, a retired army general, took the oath of office before a plenary session of the People's Consultative Assembly. The ceremony was attended by five prime ministers or heads of state and special envoys from neighboring countries, including Australian Prime Minister John Howard.
Outgoing President Megawati Sukarnoputri was absent, despite a flurry of calls from the country's political party leaders and experts for her to attend.
Yudhoyono, widely known by his initials "SBY," pledged to carry out his job and firmly uphold the country's constitution and laws.
"In the name of Allah I swear I will meet my obligations as president of the Republic of Indonesia as fully and as justly as possible," Yudhoyono said in his oath.
Also sworn in was Jusuf Kalla as the vice president.
Both Yudhoyono and Kalla held ministerial posts during Megawati's administration.
Yudhoyono was scheduled to give his inaugural address to the nation Wednesday afternoon, to be followed by the announcement of his Cabinet line-up Wednesday evening.