Authorities have repeatedly warned that such an inauguration was treasonous and that Odinga could face arrest.
However as the wording of the oath was different to that in the constitution, the consequences of this act of political theatre were unclear.
"I Raila Amolo Odinga, in full realisation of the high calling, assume the office of the People's President of the Republic of Kenya," he said in the brief and chaotic ceremony, prompting the sea of people to erupt with joy.
"We have accomplished our promise to Kenyans," said Odinga before quickly departing, the packed venue emptying out in minutes.
The ceremony followed hours of uncertainty as supporters waited in the baking sun and commentators speculated over whether the 73-year-old would actually go through with the "inauguration" that was already delayed in December.
It also came as outrage hit the media fraternity after government allegedly warned broadcasters not to cover the event, and pulled major television network Citizen TV off the air mid-morning.
"President (Uhuru) Kenyatta expressly threatened to shut down and revoke the licences of any media house that would broadcast live," the Editors' Guild said in a statement, referring to a meeting that media bosses were summoned to last week.
"The guild is appalled by the details of the meeting which was held under an atmosphere of intimidation for the media representatives present."
Odinga, a veteran opposition leader, has refused to accept Kenyatta's re-election, which came after a deeply divisive 2017 polls season in which rights activists say at least 92 people were killed.
First was an election on August 8, won by Kenyatta and then annulled in a historic decision by the Supreme Court, which ordered a re-run on October 26.
Claiming the poll would not be fair, Odinga boycotted the second vote and Kenyatta won with 98 percent.
Observers had said that the swearing-in would only further divide the nation and the crackdown on press freedom is likely to add to concerns about the state of Kenyan democracy.
While government and police had initially vowed to block the inauguration, officers kept their distance on the day.
"Let them have the park and carry on with their political activities as long as it is within the law," a senior officer said.
"We are not interested in unnecessary confrontations."
At the Uhuru Park venue, a middle-aged businessman in a suit who did not want to give his name, told AFP the swearing-in was highly symbolic.
"There is a psychological benefit that people feel their voices are heard, but more important it will mark the real start of our resistance," he said.