"In New Zealand, people aged 12 to 32 years have lower vaccination rates than young children so are less likely to be protected against these diseases. That's why teens and young adults have been most affected in the recent mumps outbreaks."
Professor of public health at the University of Otago Michael Baker said it was the culmination of decades of work to achieve high coverage of vaccinations.
"It's just a great success story for New Zealand... In the end it means a high level of safety and protection for our children."
Baker explained that the term "elimination" did not mean that no one would ever get a case of the measles, but that there had been no occurrences of a transmission of measles lasting more than 12 months in the last three years and no case of congenital rubella in 20 years.
"It essentially fizzles out. That means you don't get a sustained epidemic."
It would be impossible to prevent cases all together Baker said as some of the 3 million visitors who travel to New Zealand every year would invariably have the virus. He said measles was more infectious than both influenza and ebola.
Countries like the Philippines and China have high measles transmissions. Some people may develop measles once they arrive and infect others. But due to high levels of immunisation the virus would stop spreading.
Everyone born from January 1, 1969 needs to have two doses of MMR vaccine to be fully protected. Those born before then were likely to have been exposed to the disease so should be immune, McElnay said.
Before 2005, immunisation rates were not nationally recorded and parents might not have received reminders that their children were due for vaccination.
"Diseases like measles and most recently mumps can spread quickly in schools and tertiary education facilities," McElnay said.
"Rubella immunity is particularly important for young women thinking about starting a family because the disease can cause abnormalities for the baby."
McElnay urged people to check their medical records and get vaccinated if they weren't sure they were fully immunised.
Measles has been eliminated in the Americas, Australia, the United Kingdom and many other countries, but outbreaks occur from time to time.