George Bennett is the one road cyclist.
The women's selections were more simple.
World champion Linda Villumsen will contest the time trial, while the women's endurance team is Rushlee Buchanan, Jaime Nielsen, Racquel Sheath, Lauren Ellis and Georgia Williams.
Olivia Podmore, a junior world championship medallist, has been added to form a team sprint combination with Natasha Hansen.
"The competition within this squad has been exceptional as they have pushed each other every day in training," Cheatley said.
"I can't say enough about the efforts of Hayden Roulston, who gave up a career on the road to realise his dream of completing his career back on the track. After eight years away, the sport had moved on and he has worked tirelessly on the bike and been an invaluable leader off it."
New Zealand qualified two spots for the men's road, but Commonwealth Games medallist Jack Bauer was not nominated.
"Jack is an outstanding rider and served us well at London and Glasgow, but due to a number of significant injuries and crashes over the last 18 months we were unable to put his name forward," said performance director Mark Elliott.
The team will continue with preparations around Europe before the whole squad converges on Bordeaux for the final staging preparations next week.
New Zealand has won seven cycling medals at the Olympics with a bronze to Gary Anderson (individual pursuit) at Barcelona in 1992; gold to Sarah Ulmer (individual pursuit) at Athens in 2004; the team pursuit bronze and silver to Hayden Roulston (individual pursuit) at Beijing in 2008; and the bronze medals to the men's team pursuit and the keirin by Simon van Velthooven along with the silver to Sarah Walker in BMX at London 2012.
Full team:
Men's sprint
Eddie Dawkins, Ethan Mitchell, Sam Webster, Zac Williams.
Women's sprint
Natasha Hansen, Olivia Podmore.
Men's endurance
Dylan Kennett, Piet Bulling, Regan Gough, Aaron Gate, Hayden Roulston.
Women's endurance
Rushlee Buchanan, Jaime Nielsen, Racquel Sheath, Lauren Ellis and Georgia Williams.
Men's road
George Bennett
Women's road
Linda Villumsen
Men's mountain bike
Sam Gaze