In a statement, the Swiss tax administration said that London had received a total of 469.5 million pounds (593 million euros, $779 million), and Vienna, 738.3 million euros over the course of the year-long programme.
With the financial crisis having put Switzerland under mounting pressure to lift its trademark banking secrecy laws, the country opted to give ground in some areas in order to defend the overall principle of privacy.
Under bilateral deals with Britain and Austria, Switzerland offered two options to people who failed to declare in their home countries money placed in Swiss banks.
They could either turn themselves in to their homeland's revenue services, or have their accounts taxed by the Swiss, who then transferred the funds without naming the clients.
It was under the latter system that Switzerland handed over the sums in tranches between July 2013 and August 2014.
The completion of the payments means that the British and Austrian clients' funds are now considered clean by their homelands' tax authorities and Switzerland.
The total amount of funds regularised in this way in Switzerland now stands at 10.4 billion pounds and 5.9 billion euros.
In addition to the deal on securing back taxes, Switzerland has agreed to collect regular taxes from British, Austrian and other European Union account holders, then transfer the money to the individual's homeland anonymously.
Switzerland, which is not a member of the European Union, had also negotiated a deal with Germany to clear past tax-dodging, but it was shot down by German lawmakers.
France, meanwhile, has refused to make a similar deal with Switzerland, preferring to oblige French tax-dodgers with cash in Switzerland to use its own national system.
The deals with Britain and Austria could become redundant from 2017, when Switzerland has pledged to apply rules on the automatic exchange of tax information.
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