His decision takes effect 48 hours after he puts it in writing.
Hamas, the Islamist movement that dominates Gaza, and other Palestinian militant groups announced on Tuesday afternoon that they had accepted an Egyptian-mediated ceasefire and would abide by it if Israel did too.
Over the last 24 hours of escalated tensions between Gaza and Israel, Israeli forces targeted 160 sites in Gaza and Palestinian militants fired 460 rockets into Israel.
Earlier, the Israeli Broadcasting Corporation quoted a senior Likud official as saying that Prime Minister Benjamin Netanyahu would likely assume the defense portfolio following Lieberman's exit.
According to The Telegraph, Lieberman argued, "What we're doing now as a state is buying short-term quiet, with the price being severe long-term damage to national security".
"Behold the political slaughter dealt to leaders of the occupation who aren't capable of dealing with Gaza", it said in a statement.
"Either we come to a settlement or there's an all-out campaign".
On Wednesday, Gazan demonstrators burned pictures of Lieberman and candies were handed out in the streets, while Hamas called his resignation a "victory".More news: Mahomes sets Chiefs single-season passing TD mark
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Hamas accused Israel of "deliberate targeting of civilians and civilian facilities" in one of the most densely populated places in the world.
Residents of southern Israel had greeted news of the ceasefire with anger as dozens of protesters in the rocket-battered town of Sderot chanted "Disgrace!" at what they saw as the government's capitulation to violence and its inability to provide them with safety.
Hamas spokesman Sami Abu Zuhri said Avigdor Liberman's resignation Wednesday marked "recognition of defeat and failure to confront the Palestinian resistance".
This latest round of violence, the most intense since the 2014 war, began Sunday night after a botched Israeli intelligence gathering operation left 7 Palestinian militants and one Israeli commando dead.
Israelis from the southern city of Ashkelon demonstrate against the Netanyahu-backed ceasefire and the Israeli prime minister on November 14, 2018. "In my opinion, even if we kill 40,000 Hamas and Islamic Jihad terrorists, it is not worth losing one Israeli life".
Two of the Palestinian casualties were reportedly farmers, and the other five were militants. Since March 30, thousands of Palestinians in the Gaza Strip have gathered at weekly protests along the Israeli border to demand a lifting of an Israeli-Egyptian blockade and an improved humanitarian situation. Prime Minister Benjamin Netanyahu will take over on an interim basis.
United Nations and Egyptian mediators had been making progress in recent weeks toward informal understandings between Israel and Hamas that would ease the blockade in exchange for ratcheting down the border protests.
He also said the riots at the Gaza border will continue during the cease-fire. He also condemned the government's decision to send Qatari-bought fuel into Gaza.
Demonstrators each week have approached the border fence, throwing firebombs and grenades at Israeli troops.