Those allegations led to Mr Mahathir's surprise defection in 2016 from Barisan Nasional to join the Pakatan Harapan, saying he was "embarrassed" to be associated "with a party that is seen as supporting corruption".
Then in January, he said he would run for the leadership again.
But despite his historic win, uncertainty hangs over his tenure. Prior to his win, he intended to govern for two years before stepping down. He promised he would arrange a pardon for Anwar, clearing the way for him to be re-elected and take the top job.
Analysis: Jonathan Head, BBC South East Asia correspondent
This morning Malaysia has woken to an entirely new situation, the first transfer of power in its history, albeit to a very familiar leader. But there are huge unknowns. How willingly will Barisan Nasional, the coalition which has, in various forms, run the country since independence and embedded itself into all areas of governance, relinquish power?
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