Countries are now competing fiercely to attract today's roving rich. While London, New York and Singapore have become global "hot spots," countries in Europe and the Caribbean have also opened up special visa programs for rich investors.
"There has been an explosion in second passports as a way for these high net worth individuals to achieve global mobility," Nicolas Rollason, head of business immigration at London-based law firm Kingsley Napley, said in the report. "If you look at the Russian and Chinese high net worth communities, having second passports and a residence that gives you access to a number of countries visa-free, it is very much seen as a badge of honor."
Read MoreCities with the most millionaires per capita
The Chinese rich aren't the only ones leaving. The study found that nearly half of today's global millionaires have lived in more than one country—and many more are planning to migrate in the next five years.
Most millionaire Americans who plan to migrate are going to Europe, the study found. The largest number of millionaires planning to leave Asia are bound for North America, while millionaire migrants from the Middle East are basically split between Europe and North America.
—By CNBC's Robert Frank