The cabinet voted 20 to 2 to establish a five-member government commission into the war, chaired by a retired judge and also comprising two university professors and two retired generals.
The probe will examine how the government and defence establishments dealt with the threat from the Shiite militant group both before and during the war.
It has been established more than a month after a UN-brokered ceasefire ended the month-long offensive against Hezbollah on August 14.
State commission
Prime Minister Ehud Olmert said the government commission will have the same powers as a state commission - Israel's most powerful type of public inquiry for which many government critics here had been calling for weeks.
"The government intends to give this commission powers identical to that of a state investigative commission," Mr Olmert said at the start of the cabinet meeting.
"I very much hope that this commission will complete its work as quickly as possible and help the state of Israel confront the challenges that await us," he said.
A state commission has the power to subpoena witnesses and order police searches and has its head appointed by the chief justice of the Supreme Court.
The government commission approved on Sunday will have the same powers, but its head, retired judge Eliahu Winograd, was named by the government.
Cabinet secretary Israel Maimon said that the government inquiry will focus on drawing conclusions from the offensive, rather than determining who was to blame for the failures.
"The character of the state commission has taught us in the past that it deals mainly with establishing responsibility and blame," he said. "It is more important at this stage to draw conclusions and solve them than to seek someone's head."
Defence Minister Amir Peretz, the head of the Mr Olmert's main coalition partner Labour Party, said he was convinced the committee established Sunday would have the tools to properly investigate the conduct of the war.
Tourism Minister Isaac Hertzog said: "The commission will not give anyone any breaks and the public will give it its full backing and trust."
Failed objectives
But not everyone was convinced that the inquiry established Sunday would do the job of quelling public criticism over the Lebanon offensive.
"Only a state commission could win the trust of the public, which the
Winograd commission does not have," said Culture Minister Ophir Pines-Paz, who voted against the measure.
Gilad Erdan, a lawmaker with the opposition Likud party, told public radio: "If it's the same thing (as a state commission), why didn't they decide to set up a state commission?"
Mr Olmert and his government have come under intense criticism over the Lebanon war, which saw more than 160 Israelis killed but which failed to achieve its main objectives.
The Hezbollah militia fired nearly 4,000 rockets into Israel and the operation failed to secure the release of two soldiers seized by the Shiite militant group.
Israel has also weathered heavy criticism abroad for the devastating use of its firepower in Lebanon, where more than 1,200 people, mostly civilians, were killed and thousands of homes and infrastructure targets were bombed.
Mr Olmert, who has seen his ratings plummet because of the war, had resisted calls to set up the powerful state commission.
He said it risked completely "paralysing" the country's leadership at a time of serious threat, including from arch-foe Iran.
He initially ordered the creation of a commission to be headed by a former chief of the Mossad spy agency.
But in the face of fierce protest, both from the public and from within his own government, backed down and agreed to have a judge head the panel.