The Bank of England's new City watchdog, the Prudential Regulation Authority (PRA), said around £270 million in deposits from Laiki Bank UK had been transferred to Bank of Cyprus UK and would come under the UK compensation scheme, guaranteeing up to £85,000 per saver.
Customers, including those with current accounts in credit, will not be hit by any Cypriot levy on their accounts - potentially as high as 60% for large depositors - after the transfer and will be able to access their accounts as normal.
But customers with overdrafts will remain at Laiki, also known as Cyprus Popular Bank, and will see their accounts frozen.
The PRA, which officially came into effect on Monday under a regulation overhaul, has been working on plans for a resolution to protect UK branch customers of Laiki after Cypriot authorities announced it would shut and merge with Bank of Cyprus.
It is feared that depositors in Cyprus will be forced to accept losses of up to 60% under the European rescue package to save the country from bankruptcy.
Chancellor George Osborne said last week in a hearing with MPs on the Treasury Select Committee he wanted a solution for customers of the UK arm of Laiki.
Laiki operated as a "branch" in the UK, which meant customers would have been subject to the levy, but the transfer will see them become part of Bank of Cyprus UK - a UK subsidiary fully regulated under British rules.
Mortgage borrowers and loan customers will instead be transferred to Bank of Cyprus in Cyprus and will be contacted in due course, but should continue making repayments as normal.