"I've been informed that the immigration department is barring me and my family from leaving the country", Najib said in a tweet Saturday.
The first three ministers appointed are leaders of three of the four parties in the coalition that routed the Najib-led Barisan Nasional that had governed Malaysia for 60 years.
Mr Mahathir said he had replaced the country's attorney general, who had cleared Mr Najib of all wrongdoing in the scandal.
The announcement comes after he was defeated in general elections on Wednesday by former strongman Mahatir Mohamad, once Najib's mentor.
The coalition's defeat in the election at the hands of an alliance led by his one-time mentor Mahathir Mohamad amounted to a political quake, which toppled an increasingly authoritarian regime that had ruled the country for six decades.
This was done so that the accusations against Najib could be investigated, which Mahathir elaborated upon at a press conference.
"We are not seeking revenge", he said.
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Rumors spread Friday night that Najib would leave the country after he posted on Facebook he planned to take a "short break to spend time with my family whom I have not seen enough of in recent year".
After the ban on his travel was announced, Najib said in a Twitter message that he would respect the decision and would remain in the country.
The statement came after a flight schedule had shown that Najib and his wife were due to take a private jet to Jakarta at 10 am, according to a media report.
Mahathir, with 22 years of premiership as UMNO and BN chief, fell over with Najib since 2015 after accusing Najib of corruption related to the state investment company 1MDB.
Speaking to FMT, Mohamad disagreed with PKR vice-president Rafizi Ramli who said that talks were still pending between Mahathir and PKR de facto leader Anwar Ibrahim over the choice of Cabinet members, saying the matter had been decided at the Pakatan Harapan presidential meeting.
"We need to have this government today without delay", Mahathir, 92, said before the ceremony. I apologize for any shortcomings and mistakes, and I thank you, the people, for the opportunity to lead our great nation.
Filings by the US Justice Department in a civil lawsuit indicated almost $30 million of the money stolen was used to buy jewelry for Rosmah, including a rare 22-carat pink diamond set in a necklace.
The lawmaker said a key reason for declaring the public holidays was so that Mahathir could announce key ministerial positions and name the new adviser before trading started on Monday in an effort to reassure global investors that his government was off to a solid start.