Assoumani, a 65-year-old former military ruler turned civilian president, first came to power in a coup in 1999, before handing over to civilians in 2006.
He returned to politics and won re-election in 2016. In January, he won a vote which his opponents said was marred by fraud, but the court dismissed as inadmissible lawsuits seeking its annulment.
One person was killed and several others injured in the violence that erupted in the aftermath of the election in the country of some 870,000 people.
At his swearing-in ceremony at a partially-filled 10,000-seat stadium in the capital Moroni, Assoumani struck a conciliatory tone and pledged to work with his opponents.
"On this symbolic day, I reiterate my appeal to all the living forces of the nation, the political class, both in power and in opposition, to come together on the essentials in favour of national harmony," he said.
Congolese President Denis Sassou Nguesso and his counterparts from Madagascar, Guinea Bissau, Mozambique and Angola attended the ceremony, which some spectators described as "dull."
The opposition did not attend the event.
None of Assoumani's five presidential rivals have formally congratulated him on the victory.
Assoumani has been accused of creeping authoritarianism with his arch-rival ex-president Ahmed Abdallah Sambi handed a life sentence for high treason for allegedly selling passports.