It hopes this will stop the Swiss banking system being used by Britons to hide the proceeds of tax evasion.
Existing funds held by UK taxpayers in Switzerland will have a one-off deduction of between 19 and 34 per cent to settle past income, capital gains and inheritance tax liabilities.
Swiss banks will also make an upfront payment to Britain of £384m as a gesture of goodwill.
The deal is expected to recoup as much as £5bn for the Treasury.
From 2013, a new withholding tax of 48 per cent on investment income and 27 per cent on gains will be imposed on UK residents with funds in Swiss bank accounts.
George Osborne, Chancellor of the Exchequer, said: “We will be as tough on the richest who evade tax as those who cheat on benefits. The days when it was easy to stash the profits of tax evasion in Switzerland are over.”
The Treasury has also created a dedicated team of investigators to catch those hiding money offshore and an information sharing provision to determine who has accounts in Switzerland.
The agreement is expected to come into force in 2013.