Odinga claimed that Kibaki rigged a December 27 presidential ballot, sparking tribal fighting and police crackdowns, which resulted in the death of more than 1,200 Kenyans, displacement of 300,000 people, and a collapse of the country's tourism and agricultural sectors.
The electoral commission declared Kibaki the winner by over 200,000 votes, but independent international observers said irregularities existed.
Kibaki and Odinga held private talks on Saturday and broke a six-week deadlock over the framework of a power-sharing deal, bringing relief to Kenyans in east Africa's biggest economy.
The cabinet is tasked with redrafting a new constitution within a year, to help address long-simmering issues of land, wealth and power that fuelled the crisis.
The inauguration makes Odinga only the second prime minister in Kenyan history. Founding president Jomo Kenyatta was prime minister for a year before his title was changed.
On Wednesday, Kofi Annan, the former United Nations chief, urged Kenyans to support the new coalition government, saying the deeply divided country had a long way to go after a post-election crisis.
Annan, who mediated the power-sharing accord, said the newly-appointed coalition cabinet was a key step in resolving the crisis.
"It is another important step but we still have a long way to go," he said in the capital, Nairobi, arriving to witness the swearing-in of the cabinet.
"I believe that the next important thing is to mould the cabinet as a cohesive, effective and productive thing that will help steer this nation right.
The new government is made up of 93 ministers and assistant ministers, but Kenyans have complained that it is too bloated for a nation where 60 per cent of at least 35 million people live under a doller a day.