Serik Akhmetov, in office since September 2012, stepped down just weeks after the energy-rich nation was forced to devalue its currency, the tenge, by 19 percent against the dollar, prompting rare street protests.
Nazarbayev told lawmakers in a speech that the new prime minister, seen as promoting business-friendly policies during his previous term in office from 2007 to 2012, must work on attracting investment into the country's economy, which he acknowledged is under threat.
"Instability is growing in the global economy, the international situation is sharply worsening," Nazarbayev said as quoted by the Interfax Kazakhstan news agency.
High oil prices have kept the Kazakh economy growing, by 6 per cent last year according to World Bank estimates with growth expected to come in at 5.8 per cent this year.
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But like other emerging economies Kazakhstan has been buffeted by shifting investment flows in response to the reduction of US monetary stimulus.
It has also been affected by a slowdown in neighbouring Russia, its biggest trading partner.
"We need to use our domestic resources more to stop the threat to the economy," added the president.
Nazarbayev, 73, has broad powers to change prime ministers at his discretion, a move that automatically prompts the resignation of the entire government.
Lawmakers unanimously approved Masimov for the post of prime minister, the president's press service said.
Masimov, who has been serving as Nazarbayev's chief of staff, vowed to preserve "the unity of Kazakhs around the president" in his acceptance speech to parliament, the Interfax Kazakhstan news agency reported.