"We are all unanimous that we are going to wind up tomorrow," government negotiator Mutula Kilonzo told reporters after discussions chaired for the first time by Adeniji.
Opposition negotiator William Ruto said the "major issues are really out of the way".
"What is remaining at the moment ... how to get to a new constitution in two months and the issue of setting up a truth, justice and reconciliation commission," he said.
Parliament is due to meet on Thursday to pass a constitutional amendment to allow for a coalition government led by Kibaki. His opposition rival, Raila Odinga, will take a newly created post of prime minister.
Kibaki said the agreement was good for the country.
"We all need to come together as a united nation so that we can move forward as one," he said.
More than 1,000 people were killed and 300,000 left homeless in violence that erupted when Kibaki was sworn in as president. Odinga says he was robbed of victory.
The turmoil was expected to cost Kenya 260 billion shillings (1.92 billion pounds) in the first half of the year, according to a February 28-dated report by the Kenya Association of Manufacturers.
It said 100 billion shillings were lost in January alone, compared to the government's estimate of 60 billion.
In a "message of hope" published in the Daily Nation newspaper on Monday, Annan saluted Kibaki and Odinga for agreeing to share power and "in that single act of statesmanship, saved your beautiful country, which was about to self-destruct".
Despite the relief felt by most Kenyans, many are sceptical that the two men - who fell out when Kibaki reportedly reneged on a previous agreement to create a prime minister's job for Odinga - can overcome differences to work together.
