The figure is equivalent to the size of the US and Japanese economies combined.
The Price of Offshore Revisited was written by James Henry, a former chief economist at the consultancy McKinsey, for the Tax Justice Network.
Tax expert and UK government adviser John Whiting said he was sceptical that the amount hidden was so large.
Mr Whiting, tax policy director at the Chartered Institute of Taxation, said: “There clearly are some significant amounts hidden away, but if it really is that size what is being done with it all?”
Mr Henry said his $21tn is actually 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.