The Liechtenstein Disclosure Facility (LDF) has been extended by one year to 5 April 2016 after some 2,000 people with money invested in the tax haven came forward.
The UK taxpayers contacted HM Revenue and Customs (HMRC) after the UK authorities first struck the disclosure deal with the government of Liechtenstein in 2009.
By confessing, the individuals face penalties amounting to just 10% of the tax they have evaded.
Tax officials said that the numbers exceeded their expectations.
The LDF is an agreement with the UK and Liechtenstein governments, in which UK taxpayers with unpaid tax linked to assets in Liechtenstein can declare that tax and settle their bill with Her Majesty's Revenue and Customs (HMRC).
The LDF has run since 1 September 2009 and, by 30 September 2010, 1,721 people with outstanding tax had come forward.
Dave Hartnett, permanent secretary for tax at HMRC, said: "As the number of disclosures already exceeds the total we originally expected for the whole period of the LDF, we have agreed with the Lichtenstein government to extend the facility by one year to 5 April 2016."
Today the two governments also sign at double taxation agreement (DTA), which will ensure taxpayers of both countries are taxed fairly and both countries receive their fair share of tax revenues.
Until now, Liechtenstein had been the only European Economic Area (EEA) member without a DTA with the UK.
David Gauke, exchequer secretary, pictured, said: "This government is committed to ensuring offshore income is properly taxed.
"Today's agreement takes that commitment forward by providing greater transparency and certainty to the taxpayers of both our countries about how their incomes and gains will be taxed."
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