Cheered by thousands of singing and dancing supporters in Kinshasa, Kabila took the oath of office before members of the Supreme Court.
"I, Joseph Kabila, elected president, promise to defend the constitution and the laws of the Republic, protect the integrity of the nation and ensure national unity," he said.
Several African leaders and delegations from Europe and the US attended the inauguration of Africa's youngest president.
Ernest Musafiri, a Kabila supporter, said: "This December 6 is a day of joy for us," said
He recalled campaign promises made by the president to unite and reconstruct the country, which is a former Belgian African colony and was in a civil war between 1998 and 2003.
"We have to have confidence in him," he said.
"So be it. We bow down, but we'll be watching to see what he achieves. In five years' time, we'll give our verdict," said Norbert Kabuya.
Courthouse ceremony