A partial amnesty is to be offered to people who have evaded tax by moving their funds into an offshore account.
The Revenue has obtained details on offshore accounts
People that own up to tax evasion will pay back taxes with interest and be fined 10% of the tax owed.
However, if they do not come forward they face a full Revenue & Customs investigation and fine equivalent to 100% of any tax owed.
The Revenue has details on thousands of accounts held with the offshore branches of major EU and UK banks.
Experts have estimated that the Revenue could gather up to £1bn through this measure.
Offshore bank accounts have long been targeted by the Revenue.
UK banks and building societies have heavily marketed offshore accounts held in locations such as the Isle of Man and Channel Islands.
But some UK residents have been transferring funds offshore simply to evade tax.
This is not allowed.
UK residents can hold money offshore but it is illegal to conceal any interest earned from the Revenue.
In a series of recent legal rulings major UK banks have had to disclose details of offshore accounts to the Revenue.
Offshore account holders have until 22 June to tell the Revenue that there is tax to pay on an offshore bank account.
If account holders miss this deadline, the Revenue warn they will face an investigation and will not be able to take advantage of a partial amnesty currently on offer.
"People must come forward now. Failure to come forward will mean that we will go into full enforcement mode," a Revenue spokesman said.
"We have all the information we need and we will catch them and they could face fines of up to 100% of back taxes," he added.
Chas Roy-Chowdury, head of taxation at the Association of Chartered Certified Accountants, said that Revenue investigations often opened up a can of worms.
"People would be well advised to own up now and take advantage of the amnesty.
"Any Revenue investigation may prompt uncomfortable questions about how they came about the cash in the first place, other fines and investigations may follow.
"These people have evaded tax and the Revenue wants them back on the straight and narrow," Mr Chowdury added.
Full information about the deadline can be found on the Revenue website.