All three qualified directly through the international quota system, and will compete in different gymnastic disciplines.
The 19-year-old Schmidt will become New Zealand's first trampoline athlete to compete at the Games, while McGregor, 18, and Kudinov, 24, will take part in the women's and men's artistic gymnastics disciplines, respectively.
"When I first found out it didn't feel real and it took a while to actually sink in," said McGregor, who specializes in the vault.
"But then I did a handstand lap around the lounge," she told the New Zealand Olympic website (www.olympic.org.nz).
Tony Compier, head of the sport's representative body GymSports New Zealand, said it was largest number of New Zealand gymnasts selected to an Olympic Team since Tokyo 1964. "This is an historic day for Gymsports in New Zealand."
(Reporting by Nivedita Shankar in Bengaluru)
