Their coalition government would comprise a patchwork of small and medium parties from across the political spectrum, including for the first time in Israel's history a party that represents Israel's 21 per cent Arab minority - the United Arab List.
It would also include Bennett's Yamina (Rightward), centre-left Blue and White, headed by defence minister Benny Gantz, the left-wing Meretz and Labour parties, former defence minister Avigdor Lieberman's nationalist Yisrael Beitenu party and New Hope, a right-wing party headed by former education minister Gideon Saar, who broke away from Netanyahu's Likud.
But the fragile new government, which would command a razor-thin majority in parliament, was only expected to be sworn in about 10-12 days from now, leaving slight room for Netanyahu's camp to try and abort it by turning lawmakers over to their side and vote against it.
Israeli political analysts widely expected Netanyahu to try every possible political manoeuvre to make this happen, seizing upon Yamina members who are unhappy about joining forces with Arab and leftist lawmakers.
"Calm down. Netanyahu’s still prime minister for a few more days until the confidence vote and he's going to fight every inch of the way to deny the new government its wafer-thin majority. This is still very far from over," Anshel Pfeffer, political analyst for the liberal Haaretz newspaper, wrote on Twitter.
Netanyahu, who has yet to respond to Lapid's announcement, controls 30 seats in the 120-member Knesset, almost twice as many as Lapid's Yesh Atid party, and he is allied with at least three other religious and nationalist parties.
During a 12-year run in top office, Israel's longest serving leader has been an often polarising figure at home and abroad.
Netanyahu, 71, has sought to discredit the Bennett-Lapid alliance, saying it would endanger Israel's security - an allusion to efforts to curb Iran's nuclear programme and manage ever-fraught Palestinian ties.
Lapid, a centrist, was given the task of forming a governing coalition after right-wing Netanyahu failed to do so in the wake of a March 23 election. He campaigned under a pledge to "return sanity" to Israel, focusing on Netanyahu's corruption trial on charges which he denies.
"This government will work for all Israel's citizens, those who voted for it and those who did not. It will respect its opponents and do all it can to unites and connect all parts of Israeli society," Lapid said on Twitter.
The new government, if it is sworn in, will face considerable diplomatic, security and economic challenges: Iran, the moribund peace process with the Palestinians, a war crimes probe by the International Criminal Court and economic recovery following the coronavirus pandemic.
A source involved in the coalition talks said the proposed new government would try to retain consensus by avoiding hot-button ideological issues such as whether to annex or cede occupied West Bank territory that Palestinians want for a state.
Bennett has said that both sides would have to compromise on such ideological issues in order to get the country back on track, with government debt at 72.4 per cent in 2020, up from 60 per cent in 2019 and the deficit jumping to 11.6 per cent in 2020 from 3.7 per cent in 2019.
"This is a night of great hope," Gantz, who will remain in office under the coalition agreements, said on Twitter as he set out on a trip to Washington in the aftermath of 11 days of fierce fighting with militants in Gaza last month and as world powers press on in reviving a nuclear deal with Iran.
An end to Netanyahu's tenure may bring reprieve from unprecedented domestic political turmoil, Israel has held four elections in two years - but major shifts in Israel's foreign policy appear less likely.
After Lapid's announcement, a few dozen activists from the protest movement against Netanyahu broke out in cheers. "He's finished, he's finished, yalla Bibi, go," they chanted outside a bar in Tel Aviv, referring to Netanyahu by his nickname.
"We're hopeful for this change for a better future for this wonderful state," said 27-year-old student Eran Margalit.