The two-legged play-off has been extended by a day to take into account the huge distance between the two countries.
The delayed second leg means the playoff between the Oceania champions and the fifth placed team from South America will determine the 32nd and final qualifier for next year's World Cup in Russia.
With time differences taken into account, the two legs will be played almost five days apart.
New Zealand Football Chief Executive Andy Martin said preparations can begin in earnest now that dates have been confirmed.
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"We have been waiting for this confirmation for some time so we are pleased we can start building towards hosting Peru on November 11," Martin said.
"Now it is confirmed we can complete our preparations and look forward to one of the biggest sports events in New Zealand."
Martin said FIFA agreed to extend the gap between the two legs after considering requests from both national teams to take into account the long-haul travel involved.
New Zealand, who have never played Peru before, have been to the World Cup on two occasions, in 1982 and in 2010, while Peru have qualified for four finals but not since 1982.