Benjamin Netanyahu will vacate the Israeli prime minister's official residence within weeks, while his successor Naftali Bennett led his first Cabinet meeting on Sunday.
Mr Netanyahu's record as the country's longest-serving leader ended on 13 June, but he has remained in the heavily-guarded Jerusalem residence.
An agreement was reached on Saturday evening that requires the former prime minister to leave by July 10.
“No official meetings will be held at the residence until then,” a statement issued by the prime minister’s office said.
The announcement came after Nikki Haley, the former US ambassador to the UN, met Mr Netanyahu at the residence, according to Israeli media. She tweeted a photograph on Tuesday standing beside the opposition leader, referring to him incorrectly as prime minister.
Mr Netanyahu now has less than three weeks to leave the property, where Israelis have held weekly rallies for months calling on him to resign as he stands trial on corruption charges.
His predecessor, Ehud Olmert, told The National he moved out of the residence days after Mr Netanyahu was sworn in as leader.
"It took me four days to leave the residence of the prime minister," he said.
After 12 years in office, Mr Netanyahu remains a legislator and head of the Likud party while his trial continues in a Jerusalem court.
Mr Netanyahu will probably return to his home in the affluent coastal town of Caesarea, in northern Israel, or live in a Jerusalem flat.
Mr Bennett is expected to divide his time between Jerusalem and Ra’anana, his home city near Tel Aviv.
A week after taking office, the new prime minister presided over his first Cabinet meeting and criticised the presidential election result in Iran.
“[Ebrahim] Raisi's election is, I would say, the last chance for the world powers to wake up before returning to the nuclear agreement, and to understand who they are doing business with,” Mr Bennett said.
The ultraconservative Mr Raisi won Friday's poll following a record low turnout after his main rivals were barred from standing.
Israel is a longstanding opponent of Tehran's 2015 nuclear deal with world powers, which US President Joe Biden is trying to get back on track after his predecessor Donald Trump withdrew from the accord.
The Israeli prime minister also turned his attention to domestic affairs, with the government on Sunday approving a commission of inquiry into a crush that killed 45 people in April.
The incident during the Lag BaOmer celebrations on Mount Meron, in northern Israel, was the country’s worst civilian disaster.
An estimated 100,000 Jews had gathered at the site for the annual holiday, which is marked by lighting bonfires, when boys and men were crushed in a narrow passageway.
The government said the scope of the inquiry will include how the event was approved and the safety measures on site, although no start date for the investigation was set.
“Responsibility for learning the lessons and preventing the next disaster is on our shoulders,” Mr Bennett said.
The prime minister, a modern Orthodox Jew, also pledged to allow the Lag BaOmer celebrations to go ahead in future.
Mr Bennett's broad government contains eight factions from across the political spectrum but does not include the ultra-Orthodox parties, which are allied with Mr Netanyahu.
Along with right- and left-wing legislators, the coalition is the first to include an Arab party. The government was sworn in after four inconclusive elections in less than two years.
Well aware of the fragility of his government, Mr Bennett on Sunday urged his coalition partners to communicate directly with one another.
“The way to increase trust is that when there are misunderstandings, simply pick up the phone and call each other and resolve things quietly, without drama,” he said.