According to Netanyahu's office, the proposal was approved with ten votes against one.
Earlier in the evening, Netanyahu held a press conference where he announced that a proposal for a ceasefire would be presented to the government.
We have destroyed most of the rockets and robots. We have killed thousands of terrorists and we have destroyed the underground terrorist infrastructure near our borders, said Netanyahu then.
Furthermore, he said that he is "firmly determined" to keep Israel's soldiers alive.
"Agreement with the USA"
The USA has been primarily responsible for drafting the proposal, and Israel demands that the USA guarantees Lebanon's commitments – otherwise, Israel reserves the right to attack anyway, which Netanyahu emphasized in his speech.
He says that Israel has an "agreement" with the USA and that the country will retain its "full freedom to conduct military operations if Hezbollah tries to attack".
If Hezbollah tries to attack us, if they arm themselves and rebuild infrastructure near the border, then we will attack. If they fire rockets, if they dig large tunnels, then we will attack, says Netanyahu.
Hezbollah's side
The negotiations on behalf of the extremist militia Hezbollah were led by Lebanon's Prime Minister Najib Mikati and Speaker Nabih Berri. They have also received the blessing of Iran, the great power that supplies Hezbollah with weapons and other resources.
After Netanyahu's speech, Mikati demands that the ceasefire is implemented immediately and urges the international community to act quickly to stop the "Israeli aggression".
Although Hamas in the Gaza Strip is also closely allied with Hezbollah and Iran, the war there is not covered by these talks. The Jerusalem Post writes, however, that Israel believes that an agreement with Hezbollah would also increase pressure on Hamas, so that the prospects for a ceasefire are growing even there.
Corrected: In an earlier version of the text, there was an incorrect description of the process of approving the ceasefire.
The terms of a ceasefire in Lebanon are not yet fully nailed down, but the first phase is largely clear. It consists of a two-month transition period. During the 60 days, Israel's military will leave southern Lebanon. Hezbollah will move all its heavy weapons north of the Litani River.
A committee led by the USA will monitor that the parties do what they are supposed to. If Lebanon and others do not remove acute threats to Israel, there are reservations about the Jewish state's right to take military action.
Gradually during the two-month period, hundreds of thousands of evacuated civilians will also be able to start returning to their homes in northern Israel and southern Lebanon.