Burns was selected ahead of Cameron Bancroft to open the batting alongside David Warner, while Khawaja was expected to fill the vacant No.3 position in a 12-man squad.
Burns and Khawaja, who were included in the Test squad for this month's postponed Tour of Bangladesh, both scored centuries for a Cricket Australia XI in last weekend's tour match against New Zealand in Canberra.
Khawaja has not played for Australia since the 2013 Ashes series, while Burns played two Tests against India last southern summer.
It is a time of transition for the national side following the retirements of skipper Michael Clarke, Shane Watson, Chris Rogers, Brad Haddin and Ryan Harris.
More From This Section
The three-Test series, which will be Steve Smith's first as permanent captain, starts at the Gabba on November 5.
Chairman of selectors Rod Marsh said the squad represents an exciting new era for Australian cricket following the multiple retirements earlier this year.
"We will need to play at our best to beat a very talented New Zealand side, but we think this squad has the goods to do it and also provides an opportunity for some exciting younger players to make their mark in the Test arena," Marsh said.
"Joe thoroughly deserves his chance and was unlucky to miss out on the West Indies and Ashes tours off the back of two decent performances in his last Test match for Australia in Sydney.
"He also put in terrific performances during the recent Australia A Series in India."
Australia's group of bowlers remains unchanged from the 2015 Ashes Series in England.
"We are pleased with how our bowling unit is going at the moment," Marsh said.
"Off the back of a great bowling performance in the last Test Peter Siddle earns his selection with Nathan Lyon, a proven spin performer in the side rounding out our attack."
Australia - David Warner, Joe Burns, Usman Khawaja, Steve Smith (capt), Adam Voges, Mitchell Marsh, Peter Nevill, Mitchell Johnson, Mitchell Starc, Nathan Lyon, Josh Hazlewood, Peter Siddle.