Australia and New Zealand are developed countries with high living standards. So, it shouldn't be surprising that they have net migration into their countries. Those levels of migration are carefully controlled using points systems that prioritize highly educated and skilled people who are of value to the country.
The most common origin country is the United Kingdom, since they have strong ties to the UK from the days of the British Empire. They remain commonwealth countries to this day, and still have the Queen on their currency. Between 2004 and 2013, the UK was the greatest source of immigrants to New Zealand, though India and China finally overtook the UK in 2014. It's a similar story in Australia, where only India and China regularly beat the UK in immigration.
Clearly, there are no physical geographical reasons for this migration, since the UK is almost exactly on the opposite side of the world from Australia. People definitely aren't moving from the UK out of convenience. Since most migration to and from both countries relates to reuniting family, migration out of Australia and New Zealand is generally to these same three countries. Nearby countries, like the Philippines and Fiji, are also significant.
Migration to Australia continues to increase year by year. The government limits and quotas are being increased, but this is in response to demand. Without limits, immigration would no doubt be much higher. Immigration in New Zealand has been fairly static numerically, though it saw a significant increase in the early 21st century. Some might argue that this was partly due to the Lord of the Rings movies, which brought the beauty of the country to the attention of people abroad; certainly, it had a dramatic impact on tourism to the country.
