FOR FOREIGNERS, it used to be that hard work and plenty of patience for bureaucratic red tape would garner access into a coveted country. But, these days, sometimes all it takes to grab that golden ticket is achieving multimillionaire status and promising to make a hefty investment in a new homeland.

Countries such as the United States, Australia and New Zealand are all embroiled in a global tug-of-war for the wealthy, and each has either rolled out or reauthorized what are known as millionaire visas in recent years. These programs, which are aimed squarely at wealthy investors, fast-track these individuals' path to permanent residency—and sometimes even citizenship. "Countries are trying very hard to attract foreign millionaires or billionaires," says Douglas Goldstein, an international investment adviser and director of Profile Investment Services, which is based in Israel. "Everyone wants these people to bring their money and spend there."

This push comes at a time when the growth in global wealth is shifting to business tycoons and others from emerging markets. The world's "super rich"—those with at least $100 million in disposable assets—is forecasted to grow between 7 percent and 24 percent through 2016 in Western Europe and North America, much less than the 60 percent forecasted in Latin America, 76 percent in Russia and more than 100 percent in China and India, according to a 2012 wealth report from Knight Frank and Citi Private Bank. At the same time, legal experts and financial advisers say, political uncertainty in some places, as well as the ongoing tremors being felt in the Middle East, has pushed more multimillionaires to seek refuge in nations like the U.S. "They're coming here for social and economic stability," says Bruce Givner, an attorney based in Los Angeles.

To grab some of this wealth, officials in Australia say they launched their so-called significant investor visa last year to try and "attract prominent business people and investors from across the globe and increase economic growth." Folks who want to soak in the Sydney sun and become permanent residents can do so in exchange for meeting certain criteria, including investing at least $4.7 million in financial products like bonds and managed funds, as well as companies based on the far-flung continent. The program has already attracted more than 170 applicants—who are mostly from China—and similar ones elsewhere have also seen a surge in demand of late. Last year, around 7,600 foreigners applied to the immigrant investor program known as the EB-5 in the U.S., more than double the number who did so in 2011.

Like the gold "flash pass" available at some amusement parks, investors can pay extra to skip ahead of others who are already fast-tracking through a line. In the United Kingdom, around $1.5 million in investments helps qualify for permanent residency after five years, while spending about $15.6 million cuts that wait to just two years. A bigger investment can also make it easier to get that coveted stamp of approval from an immigration and customs office. A "regular" investor visa in New Zealand requires, in part, that foreigners hold at least three years of business experience, speak English and be younger than 65 years old. But the country's government legislated easier requirements two years ago. Now, an upgrade to investor "plus" status—which is obtained by spending an additional $6.8 million or so on top of the $1.2 million that regular investors pay—means applicants can have zero business experience, speak any language they want and be an octogenarian, or any other age for that matter. Welcome to Kiwiland.