"For the first time in our history people have gathered here in their hundreds of thousands to say enough is enough on election-rigging", Odinga said.
He called the ceremony a step towards establishing a functioning democracy in Kenya.
Odinga defied a government ban on the event and government warnings that the move would be treasonous.
Hours later, the government outlawed the opposition's National Resistance Movement, with Interior Minister Fred Matiangi declaring it an organized criminal group.
Odinga was sworn in as people's president in the oath administered by Ruaraka Member of Parliament TJ Kajwang' and former Nairobi gubernatorial aspirant Miguna Miguna. The opposition claims Kenyatta, who officially took office as president in November, is illegitimate.
On Monday, Linus Kaikai, chairman of the Kenya Editors Guild, said senior editors had been summoned by the authorities and warned not to cover the event or risk being shut down.
Meanwhile, Kenyan authorities shut television and radio stations yesterday in response to Odinga's presidential oath taking.
The announcement by the National Super Alliance sets the stage for another round of election-related clashes between police and opposition supporters and raises fears of more civilian deaths.
Government officials had declared the "swear in" as an act of treason.
The court ruled the results from the August election were "null and void" and ordered a fresh vote in October which Kenyatta won after Odinga boycotted, citing a lack of electoral reforms.
Tension has been brewing in Kenya following nullification of results of a presidential election held in August past year by the Kenya Supreme Court which also called for a re-run that was boycotted by Odinga.
The election had been controversial from the outset.
After boycotting October's election rerun, Odinga has continued to contest the president's legitimacy, culminating in today's ceremony.
Asked how Kenya will be run with two presidents, NASA's chief executive officer Norman Magaya was unequivocal: "Kenya will not have two presidents", he said. They said the numbers came from the government's electoral servers - an assertion the electoral commission has denied.
Kenyan police have always been accused of using excessive force to crush political dissent and protests, according to human rights groups who have further stated that Kenyatta is moving towards a dictatorship. We should not forget that the global community observed the Kenya election and it was adjudged free and fair.
Many hoped Mr Kenyatta would reach out to his rival.
The Supreme Court in a landmark ruling annulled the elections after NASA proved that the process was not clean.