The Asia-Pacific region is now home to 3.37 million high net worth individuals (HNWI) - people with $1 million or more to invest - compared with 3.35 million in North America and 3.17 million in Europe, the firms said in a report.
Asia's wealthy - 54% of whom are concentrated in Japan, almost 17% in China and more than 5% in Australia - saw their total fortunes slip to $10.7 trillion last year from $10.8 trillion in 2010, and lag North America's $11.4 trillion.
The Asia-Pacific Wealth Report, compiled by Capgemini and RBC Wealth Management, is closely watched by wealth managers, high-end property agents, luxury goods retailers and other businesses for signs of how and where the ultra-wealthy are investing and how their fortunes are faring.
Many of Asia's rich made their millions and billions through family businesses and property.
"We don't see massive shifting in the allocations of portfolio management," Claire Sauvanaud, vice president of Capgemini Financial Services, told a news conference.
Wealth fell most significantly last year in Hong Kong (20.1%) and India (18%) and grew most strongly in Thailand (9.3%) and Indonesia (5.3%). Growth was more modest in Japan (2.3%) and in China (1.8%).
Weakness in Europe and other global trends played their part in the slight fall in total Asian wealth, the report said, but the "region grappled with its own economic challenges, including inflation, slowing growth and capital outflows."
"Nevertheless, Asia-Pacific is expected to continue showing stronger growth than other regions going forward, and its HNWI population and wealth are likely to keep expanding," it said.
As part of that, Asia's rich are looking more to offshore wealth centres close to home, such as Singapore and Hong Kong, in search of wider access to products and services, tax advantages and financial confidentiality, the report said.
Challenges for the offshore wealth management industry include a scarcity of skilled talent, lower profitability, and the costs of compliance and restrictions on services due to higher regulatory scrutiny, it said.
Diversity of the backgrounds and expectations of rich clients means there is more demand for tailored products and a greater desire to play an active role in managing their portfolios, the report added.