He also announced - to cheers among his supporters - that there would be a two-day public holiday, adding: "But there will be no holidays for the winners."
The official results showed the opposition Pakatan Harapan - the Alliance of Hope - secured 113 of the 222 seats being contested, including some which have only ever been held by the government. BN took 79 seats.
Rising living costs and long-running allegations of corruption weighed heavily on many voters and saw them peel away from Mr Najib and his once unshakeable coalition.
"I feel that with this change we probably can see something better in the future," Suva Selvan, a 48-year-old doctor, told AFP.
"Our hope for the future is a better government, fair, free and united."
Mr Mahathir was prime minister, at the head of the BN coalition, for 22 years, from 1981 until he stepped down in 2003.
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