Holding a Bible in his right hand at a park in Nairobi, Mr Odinga declared that he was answering to a “high[er] calling to assume the office of the people’s president of the Republic of Kenya”.
“People had had enough of election rigging and the event was a step towards establishing a proper democracy in the East African state,” Mr Odinga told a cheering crowd.
Speaking earlier to Kenyan broadcaster KTN, Mr Odinga said his “swearing-in” was intended to “show the world that what we are doing is legal, constitutional and not something you can remotely describe as a coup”.
Mr Odinga turned up for just 20 minutes. He signed a statement, swore an oath and left the stage, leaving his supporters wondering why it was such a low-key affair.
His deputy, Kalonzo Musyoka, was not at the event, and Mr Odinga said Mr Musyoka would be “sworn-in” at a later date.
Three privately owned television stations – NTV, KTN and Citizen TV – went off air from around 09:10 (06:10 GMT) as authorities forced them off the air over plans to cover the gathering.
Some still covered through live streaming on their website, YouTube and Facebook. A move Kenyan journalists described as “respect of the constitution” and an end to the “unprecedented intimidation of journalists”.
Uhuru Kenyatta won the original election on 8 August but that result was annulled by the Supreme Court, which described it as “neither transparent nor verifiable”.
He was officially re-elected with 98% of the vote on 26 October but just under 39% of voters turned out. He was inaugurated in November.
Odinga had urged his supporters to shun the re-election because he said no reforms had been made to the electoral commission.
Correspondents say the election dispute has left Kenya deeply divided. About 50 people are reported to have been killed in violence since the August ballot.