The statement by centrist Lapid and his main partner, nationalist hardliner Naftali Bennett, came about 30 minutes before a midnight deadline to put together a new governing coalition following the March 23 elections.
An official statement issued by President Reuven Rivlin's office said that Lapid informed the president that "he has been able to form a government."
Under the coalition deal, Lapid, leader of the centrist party of Yesh Atid, and Naftali Bennett, leader of the nationalist party of Yamina, will rotate the premiership, with Bennett serving first as prime minister, according to the statement.
The new coalition also includes Ra'am, an Islamist party headed by Mansour Abbas, marking the first time an Arab party is part of a coalition in Israel.
The coalition would be comprised of a diverse coalition of additional small parties, including the centrist Blue and White party, headed by current Defense Minister Benny Gantz that partnered with Netanyahu to form the outgoing government, the right-wing parties of Israel Our Home and New Hope, the centrist-left party of the Labor and the leftist Meretz party.
The president congratulated Lapid and other heads of the parties on the government. He said that he expects the Knesset (parliament) "will convene as soon as possible to ratify the government, as required."
Israel's Ha'aretz newspaper reported that the Knesset is expected to be convened for a confidence vote for the new government by next Wednesday.
Lapid wrote on Twitter that the new government "will work in the service of all Israeli citizens, those who voted for it and those who did not. It will respect its opponents and do everything in its power to unite and connect all parts of Israeli society."
The move comes amid a series of inconclusive elections and a lingering political deadlock.