Primary election deal
Under Wednesday's accord, Olmert agreed to Barak's demand that primary elections be held in Kadima by September 25.
In turn, Labour will not back the efforts of the Likud opposition to bring down the government, the parliamentary sources said.
David Chater, Al Jazeera’s correspondent in Jerusalem, said: "This huge battle of the egos between the two politicians has been resolved and perhaps now they can concentrate on so many other things that are going on at the moment [such as the truce in Gaza between Israel and Palestinian groups]."
Without Labour’s support, Olmert's coalition would not have the required 61 seats for a majority in the 120-member parliament.
Barak earlier this month threatened to quit Olmert's coalition government.
He said he would abandon the coalition if Olmert did not resign over suspicions he had illegally accepted cash from a US businessman before he became prime minister in 2006.
Olmert has admitted that he received payments from Morris Talansky, a US financier, when he was running for the mayoralty of Jerusalem and key positions in the Likud party, but argues that they were legal campaign contributions.