The portfolio was previously headed by ousted Prime Minister Najib Razak, who was handed a thumping defeat by Mahathir's alliance in Wednesday's general election. "So based on this principle I have chose to give up both positions".
The finance minister has been an ethnic Muslim Malay since 1974 and the appointment of Lim, a chartered accountant who led the wealthy northern state of Penang since 2008, reflects reforms pledged by Mahathir's alliance to heal racial divisions in the country blamed on decades-old preferential policies.
Malaysia's new Prime Minister Mahathir Mohamad has announced that politician Anwar Ibrahim, who was jailed after falling out with the government, will receive a full royal pardon from the country's king.
Mahathir's comments appeared created to counter worries among investors who had bet that former leader Najib Razak would stay in power. New Prime Minister Mahathir Mohamad said he thought he could recover most funds from 1MDB and that Najib will pay the consequences if the law finds any wrongdoing. "But we want to be neutral (with the other countries)", he said.
Filings by the US Justice Department in a civil lawsuit indicated almost $30 million of the money stolen was used to buy jewellery for the prime minister's wife, Rosmah, including a rare 22-carat pink diamond set in a necklace. "I respect the decision and I will remain in the country with my family".
"I have been informed that the Malaysian immigration department will not allow my family and me to go overseas", Najib said in a tweet.
He confirmed he had ordered the travel restrictions on Mr Najib, and cited "whatever little information that justifies ourselves taking action, including detention, arrests or even preventing them from going abroad".
The ASEAN consists of Brunei, Cambodia, Indonesia, Laos, Malaysia, Myanmar, the Philippines, Singapore, Thailand, and Vietnam.
Mahathir is expected to name cabinet members to head 10 key ministries, including finance, foreign affairs, defense and home affairs, on Saturday.
Mahathir said Malaysia's king had agreed to pardon Anwar, who was jailed in 2015 for sodomy in a conviction that he said was politically motivated.
Mahathir ruled Malaysia between 1981 and 2003, overseeing the country's transformation into an industrialized nation and guiding it through the Asian financial crisis of two decades ago.
He redeemed himself in 1974, after writing a controversial book called The Malay Dilemma about the marginalisation of the Malay population, and UMNO invited him back as minister of education.
He emerged from political retirement in anger at the corruption scandal at 1Malaysian Development Berhad (1MDB), a state investment fund by Najib, his former protege.
What followed was a major investigation by the Wall Street Journal, which reported it had seen a paper trail that allegedly traced close to $700 million from the fund to Najib's personal bank accounts.
Dr Mahathir Mohamad, making the announcement at a press conference held at the Al-Bhukary Foundation here, said Datin Seri Dr Wan Azizah Wan Ismail is the deputy prime minister as decided earlier.