The Central Election Commission said that polls had opened across the Central Asian country at 0200 GMT for a vote analysts say is likely to see the changes passed.
Kyrgyzstan, a mountainous majority-Muslim republic of six million, is the most democratic of the so-called "stans" but also the most politically volatile.
In just 25 years of independence the country has experienced two revolutions unseating presidents in 2005 and 2010 as well as ethnic violence.
If passed, the country's prime minister will gain new powers over budget-related legislation and will not need parliamentary or presidential approval to appoint and dismiss ministers.
Atambayev has repeatedly denied accusations he will drop down into the strengthened premier's role when his single six-year term ends next year.
A by-law created when the constitution was last amended in 2010 said the existing constitution should remain until 2020 but parliament and the judiciary endorsed the vote.
One highlighted by the Council of Europe's Venice Commission defines marriage as "between a man and a woman" rather than "two persons" as previously.
Another amendment rights groups have railed against removes the government's obligation to consider the opinions of international rights bodies regarding citizens' complaints of rights violations.
Critics have argued the government has not explained the changes to the public, but backing from pro-government media and the absence of an effective 'no' campaign means they are likely to pass.
Bolot Osmonov, 58, who works as an engineer in the capital Bishkek said he would vote in favour of the amendments today.
Kyrgyzstan is one of the two poorest countries to emerge from the former Soviet Union with a strong dependence on cash transfers sent home by hundreds of thousands of Kyrgyz in Russia.
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