The figure is equivalent to the size of the US and Japanese economies combined.
The Price of Offshore Revisited was written by James Henry, former chief economist at the consultancy McKinsey, and commissioned by the Tax Justice Network.
He said $21tn is a conservative figure and the true scale could be $32tn.
Mr Henry used data from the Bank of International Settlements, International Monetary Fund, World Bank, and national governments.
His study deals only with financial wealth deposited in bank and investment accounts, and not other assets such as property and yachts.
The report comes amid growing public and political concern about tax avoidance and evasion. Some authorities, including in Germany, have even paid for information on alleged tax evaders stolen from banks.
The group that commissioned the report, Tax Justice Network, campaigns against tax havens.
Mr Henry said that the super-rich move money around the globe through an "industrious bevy of professional enablers in private banking, legal, accounting and investment industries.
"The lost tax revenues implied by our estimates is huge. It is large enough to make a significant difference to the finances of many countries.
"From another angle, this study is really good news. The world has just located a huge pile of financial wealth that might be called upon to contribute to the solution of our most pressing global problems."
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