Greek taxpayers with funds in other countries will be allowed to declare it without penalty and to pay a reduced rate if tax on it.
The initiative is designed to lure money back to Greece which is struggling with a cash crunch threatening to turn the country bankrupt.
"The government will table a bill to allow citizens to voluntarily declare their deposits abroad," Finance Minister Yanis Varoufakis told reporters after meeting Swiss officials in Athens.
Billions of euros have left Greece since the start of the financial crisis and talk about Greece leaving the eurozone.
Consequently Greek banks have faced a struggle without cash and have turned instead to the central bank for funding.
Under the planned law, the deposits may be taxed at a rate of 15 to 20%, a senior finance ministry official said, an incentive for those who have sent money abroad but have not reported it as income to Greek tax authorities.
Depositors who have evaded reporting incomes would otherwise face a 46% tax rate and 46% fine if caught.
Varoufakis said that once the bill is passed by parliament, a political agreement will be signed between Greece and Swiss authorities to exchange information on Greek deposits held in Swiss banks.
"We have an agreement with the European Union about an automatic supply of information and this will be applied for Greece as well," said a Swiss official.
"We want to support Greece in this effort."
