Najib, 64, said he was taking a short trip to spend time with family, but it didn't matter: Malaysia's government prevented him and his wife Rosmah Mansor from leaving the country.
There had been widespread speculation Najib would fly overseas after his shock election defeat this week, amid calls for him to be prosecuted over the sprawling 1MDB corruption scandal. "So based on this principle I have chose to give up both positions", Najib said.
Earlier this week, Mr Najib's long-ruling Barisan.
Mahathir also said Saturday that the future of jailed opposition leader Anwar, whose support in the opposition coalition helped oust Najib, would be determined by the party.
On the economic front, Mahathir vowed to cancel a goods and service tax imposed since 2015 and said the government could also renegotiate the terms of Chinese loans for infrastructure projects.
Nearly $700 million ended up in Najib's personal bank accounts, although the attorney-general said it was a donation from the Saudi royal family and cleared the then-premier of misconduct.
Malaysian markets were closed on Thursday and Friday for public holidays announced by Mahathir after the election, but overseas investors were nervous about Najib's ouster after a decade in office and the ringgit lost four percent in offshore trading before stabilising on Friday.
Following the announcement of the ban, Najib said he and his family would respect it and stay in the country.
The adviser would be appointed to "restart the 1MDB probe and bring back the money", said one of the sources, who worked closely with Mahathir's campaign team.
Mr Najib denies any wrongdoing.
Former PM Najib Razak and his wife have been blacklisted from leaving the country which he recently led, as he is accused of stealing $700 million from state funds. "What we want is to restore the rule of law. if the law says that Najib has done something wrong, then he will have to face the consequences".
Mr Mahathir, who was due to name his cabinet later on Saturday, has indicated that Mohamed Apandi would be axed for hiding evidence of wrongdoing.
Najib also tweeted that he hoped the "divisive period" in the country's history would end with unity.
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. I apologize for any shortcomings and mistakes, and I thank you, the people, for the opportunity to lead our great nation.
"We need to do investigations on a lot of things", Mahathir said on Saturday in Kuala Lumpur.
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