Mr Anwar and Dr Mahathir, former allies and then implacable foes, joined hands to contest this week's election and oust the administration of Najib Razak.
If Najib had stayed in place, 1MDB's survival could have been dragged out, said Ismael Pili, Singapore-based co-head Asian bank research at CreditSights.
People stood on roadsides waving the white, blue and red flag of the opposition alliance that triumphed in Wednesday's election. However, he has pledged to grant jailed opposition icon Anwar Ibrahim a royal pardon and eventually pass the premiership on to him.
Supporters of the incoming government took to the streets of Kuala Lumpur to celebrate the unexpected victory.
"I am very happy to note that when I met my husband he was in a jubilant mood", Wan Azizah said on Friday, according to Malaysia's Star newspaper.
The new governing coalition Pakatan Harapan is led by Mahathir Mohamad, who was prime minister from 1981 to 2003 as UMNO and BN leader.
In addition to naming Lim Guan Eng, a former state chief minister, as finance minister, Mahathir also named former Deputy Prime Minister Muhyiddin Yassin as home affairs minister and Mohamad Sabu as defense minister.
Najib's downfall was fueled by the imposition of a sales tax that mainly affects the rural poor and a corruption scandal in which billions of dollars were allegedly stolen from a state-owned investment fund he oversaw.
Mahathir Mohamad was sworn in as Malaysia's seventh prime minister on Thursday after a stunning election comeback, defeating the coalition that has ruled the nation for six decades since independence from Britain.
US investigators said Najib's associates stole and looted $4.5 billion from the fund, of which some $700 million landed in Najib's bank account and some $30 million used to buy jewelry for his wife.
But Chin said it was unlikely anything would happen to Najib immediately with regard to 1MDB, as the new government would want to show it was following due process.
Before Anwar, 70, can serve in a high office, Mahatir said, he'll need to become a member of Parliament - and, he warned, "That might take a long time".
He plans to cancel an unpopular goods and service tax and has criticised a "fake news" law brought in by the National Front before the election.
Mahathir disputed Najib's assertion during a concession speech that Malaysia's king must appoint the new prime minister because no single party has a parliamentary majority, calling it "confusion".
Najib, 64, said he accepted the "verdict of the people". "BN is committed to the principles of democracy", he added.
Newly minted PM Mahathir has vowed to launch investigations into sovereign wealth fund 1MDB.
"He in fact has hidden evidence of wrongdoing and that is wrong in law", he said.