In a pre-recorded television address, he said the decision had "not been simple".
Mr Nazarbayev, 78, has been largely unchallenged since he became president of the oil-rich nation in 1990.
He has focused on economic reform while resisting moves to democratise the political system.
"I have decided to give up my powers as president," he said during a surprise television address.
Mr Nazarbayev said the speaker of the upper house of parliament, Kassym-Jomart Tokayev, would take over as acting president for the remainder of his term.
The announcement comes just weeks after the leader sacked the country's government, citing failures to improve the economy.
"In many areas of the economy, despite the adoption of many laws and government decisions, positive changes have not been achieved," he said in a statement at the time.
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