While the account has no set up or monthly fees, TransferWise charges a fee every time a person changes their money into a different currency for which it uses the mid-market rate.
It offers the abililty to transfer money into more than 40 currencies but claims its fees are five times cheaper than banks and nine times cheaper than online rival Paypal.
TransferWise has also signed an integration deal with Kiwi company Xero meaning transactions from the borderless account will be imported directly into the accounting software, making it easier for businesses to track their transactions.
Tech entrepreneur Hinrikus set up TransferWise in 2011 after feeling frustrated at the fees he had to pay to move his money between curencies using banks and the time it took.
Estonian-born Hinrikus was working for Skype as the tech company's first-ever employee in the early 2000s in a role which required a lot of travel across Europe.
The 37-year-old was being paid his monthly salary into his Estonian bank account, but frequently needed to transfer that money into local currencies when he was working in other countries for longer stints.
After transferring euros into pounds during a long stay in London, Hinrikus was shocked to discover he was losing a fortune in bank fees and poor exchange rates, despite the transfer being a quick and easy task for bank staff.
While he was in London, Hinrikus met fellow Estonian Kristo Käärmann who had the same problem but in reverse, as he was being charged excessive fees transferring pounds to Estonia.
The pair soon set up a simple plan to avoid the bank fee rip off.
"The next month I sent money from my account in Estonia to his in Estonia and vice versa with our London accounts at the best exchange rate and boom — it worked."
Hinrikus and Käärmann ended up saving "thousands of pounds" using that trick, and soon let a few friends in on the secret before deciding to set up the business.
Over four million people use TransferWise's international money transfer platform to send over £3 billion every month.
The company employs 1300 people globally in 11 offices and has a 15 per cent market share in the UK, its most mature market.
TransferWise grew it's revenue by 75 per cent last year and has been profitable for two years.
Hinrikus said it launched the debit card for consumers in the UK in August and already US$2 billion had gone into borderless accounts encouraging it to expand the offer to business customers and globally.
"We are rolling it out globally because of the success."
Hinrikus said most people who used its service were referred by a friend.
Like banks it must follow the same anti-money laundering rules and it is a registerd financial institution.
He said the business was also well-capitalised.
