The king has already given his consent for Najib to be sworn in as prime minister, and he is expected to take the oath of office, loyalty and confidentiality at the palace in Kuala Lumpur on Friday morning.
Abdullah, who took office in 2003, was pressured to step down following a dismal performance by the ruling Barisan Nasional (BN) coalition in last year's general elections.
He is likely to be remembered for allowing more public freedoms than his predecessor Mahathir Mohamad, who was known for his semi-authoritarian rule during his 22 years in office.
But he also failed to fulfil promises to eradicate corruption, reform the judiciary and strengthen institutions such as the police and the civil service.
Earlier this week Abdullah told Malaysian media editors that his time in office was marked by "missed opportunities", and that the poor electoral showing in 2008 was his biggest regret.
The BN, which has been in power since independence in 1957, failed to maintain its two-thirds majority in parliament for the first time in 40 years, and also lost control of an unprecedented five states.