Mr Koroma, the opposition leader, won 54.6% of the final vote against Vice-President Solomon Berewa's 45.4%.
Thousands of jubilant opposition supporters danced in the streets of the capital as news of his victory spread.
But police fired tear gas to disperse looters at the former ruling party's headquarters in Freetown.
One person is reported to have died.
The national election commission said that flaws in the vote were not enough to invalidate the result.
PROFILE
Mr Koroma was sworn in at an afternoon ceremony in Freetown, attended by military officials and dignitaries including outgoing President Ahmed Tejan Kabbah and Mr Berewa.
Thousands of opposition supporters, bedecked in red, sang and danced throughout a heavy downpour.
Mr Koroma told the crowd: "My government will spare no effort to deal with zero tolerance with corruption and mismanagement of state resources.
"We know how high your expectations are and that you have suffered for too long."
Mr Kabbah, who was prevented by law from running for a third five-year term, said: "I inherited a bankrupt, war-torn and failing state.
"Today, I am handing over to you a fully stable and functional state."
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Last week, the national electoral commission was asked to investigate reports of suspect ballots at 14 polling stations, where the turnout was reported as 100% or more, compared to a national average of 68%.
Amid such concerns the governing Sierra Leone People's Party (SLPP) sought an injunction to try to stop the publication of any further results.
But by the time the High Court looked at the application and deemed it required resubmission, the result had already been announced.
In any event, the electoral commission had pointed out that most, though not all, of the suspect results were in SLPP strongholds.
Inroads
Ernest Bai Koroma, 54, is an insurance broker who says he wants to run the country like a business concern.
He polled well in the predominantly Muslim north of the country and in the capital, Freetown.
But he also made inroads into his opponents' traditional heartland in the ethnic Mende south.
Sierra Leone is gradually rebuilding after a decade-long, diamond-fuelled war but remains one of the world's poorest countries where mass unemployment could still lead to instability.
Mr Koroma leader ran a slick campaign calling for change.
Opponents say his party mismanaged the country for two decades leading up to the war but such criticisms were not enough to deflect an electorate seeking a change.
His rival for the presidency, Mr Berewa, had been a surprise choice - named as the SLPP candidate by the incumbent President Kabbah at a time when he was not even a card-carrying member of the party.
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