"We have seen the good results of our efforts to build good government and fight against corruption but it still needs improvement.
"We also have decreased the number of poor but need to continue for people's welfare. I believe achievements that we have made will create new challenges," added Yudhoyono.
Tuesday's event was attended by foreign dignitaries including leaders of Australia, Brunei, East Timor, Malaysia and Singapore, as well as senior officials from around the world.
The ceremony was held under tight security at the People's Consultative Assembly building in the city centre, where about 20,000 police backed by armoured vehicles were on hand to secure the area.
|Regional leaders attended the ceremony in Jakarta under tight security [EPA]
Yudhoyono defeated former president Megawati Sukarnoputri in 2004 to become the country's first directly-elected leader since the fall of late Suharto in 1998.
He repeated his victory in July against Megawati and Jusuf Kalla, his vice-president, to become the first Indonesian leader to be democratically re-elected.
In his inauguration speech, Yudhoyono said Indonesia can still register positive growth despite being in the middle of the economic crisis.
"The essence of our programme for the next five years is to improve welfare, strengthen democracy and the legal system.
"But we cannot stay idle, as our tasks are far from over. Just like a ship moving forward, we will head through an ocean full of waves and storms," he warned, referring to volatile crude oil prices and stagnant investment.
The government has predicted economic growth of 4-4.5 per cent this year, third only to China and India in the G20 club of rich and major developing countries.
Indonesia's economy grew 6.1 per cent in 2008.