He said Thursday and Friday would be public holidays, another slap for Najib, who on election eve had promised public holidays if his coalition won.
Official results show the opposition parties, which banded together as the Alliance of Hope, surpassed the 112 seats needed for a majority in parliament.
Malaysia's opposition alliance headed by veteran ex-leader Mahathir Mohamad, 92, has won a historic election victory, official results showed on Thursday, ending the six-decade rule of the Barisan Nasional (BN) coalition.
Mahathir Mohamad holds up a document during a news conference following the general election in Petaling Jaya, Malaysia, May 10, 2018.
The election result is a political quake for the Muslim-majority country, ending the National Front's unbroken 60-year rule and sweeping aside Najib, whose reputation was tarnished by a monumental corruption scandal, a crackdown on dissent and the imposition of an unpopular sales tax that hurt many of his coalition's poor rural supporters.
Faced with a leadership challenge after just five years in office, Mahathir detained more than 100 opposition politicians, academics and social activists without trial, under internal security laws. "There is a lot of work to be done". "We would like to announce it as quickly as possible as well".
"We expect today for me to be sworn in as prime minister", he told a press conference, addressing concerns over a delay by saying that some "confusion" over the process had now been cleared up.
Few had expected Dr Mahathir to prevail against a coalition that has long relied on the support of the country's ethnic-Malay majority.
However, he added that "because no party got a simple majority, the king will decide in a while who will get the confidence of the parliament".
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People stood on roadsides waving the white, blue and red flag of the opposition alliance that triumphed in Wednesday's election. Cars honked their horns as they sped past.
"We trust the wisdom of the King to make the best choice", he said, in an indication that he was stopping short of conceding power. Mahathir said he would seek a pardon for Anwar.
When Mahathir was prime minister in the 1990s, Anwar was jailed on sodomy and corruption charges that critics said were politically motivated.
Malaysia's king will grant Mahathir Mohamad an audience at 5 pm (0900 GMT), Saifuddin Abdullah, a leader from Mahathir's aliance said on Thursday.
"I have to manage four presidents of four different parties", Mahathir said.
"No such meeting took place", said the 64-year-old leader, calling the election a "tough clash" marked by "slander" against his government.
He was never far from the headlines in retirement, and two years ago he came back to active politics, this time in the ranks of the opposition, vowing to oust his protégé Najib Razak from the prime minister's chair over a financial scandal at the state investment fund 1Malaysia Development Berhad (1MDB). He denies any wrongdoing.
Dr Mahathir was credited with modernising Malaysia during his time as leader but was also known for his heavy-handed approach, which saw opponents imprisoned and courts subjugated.