The formation of a power-sharing cabinet is the key element of a deal to end the east African nation's post-election crisis in which 1,200 people died and more than 300,000 were displaced.
There were no immediate details about the make-up or size of the cabinet, nor about whether either side gave up on claims to influential ministries they had haggled over.
Spokesmen for Odinga's Orange Democratic Movement (ODM) and the government declined to comment.
The two leaders had agreed to announce a coalition cabinet on April 6. But the deal fell apart at the last minute, unsettling Kenyans and investors fearful of a return to violence.
Over the past week, Kibaki and Odinga have urged calm and said their positions were not that far apart.
However, both refused to budge and said it was the responsibility of the other.