The exchange is one of many that swaps bitcoins, computer generated cash, for real world currencies.
The change in status makes it easier to use bitcoins and bestows national protections on balances held at the exchange.
Bitcoins, and the global network of computers that supports them, first appeared in 2009 and since then it has become a very widely used alternative payments system. Many people "mine" the coins by participating in that network and a growing number of web stores and online firms accept bitcoins as payment. One bitcoin is currently worth about £8 ($13).
Under European laws, the deal means Bitcoin-Central becomes a Payment Services Provider (PSP) that has an International Bank ID number. This puts it on an equal footing with other payment networks such as PayPal and WorldPay. As a PSP it will be able to issue debit cards, carry out real-time transfers to other banks and accept transfers into its own coffers.
The deal was a "significant" step towards legitimacy for Bitcoin, said Vitalik Buterin, technical editor of Bitcoin magazine.
Before now, he told the BBC, it had been hard for novices to get started with bitcoins. The links that Bitcoin-Central, and other exchanges who have also applied to be PSPs, will have to the global banking system will make that much easier as it will become possible to transact with a bitcoin account just like any other bank account.
It also means, he said, that deposits held at Bitcoin-Central would be backed by the same compensation laws and schemes that apply to cash held in other bank accounts. However, he said, this protection only applied to balances held in euros rather than bitcoins.
The move could convince many organisations and businesses to start accepting bitcoins as payment, he said.
"The more we see governments and banks being willing to deal with Bitcoin, the more comfortable a lot of organisations are going to be making the step forward themselves," he said.