Thinkmoney will become the first account provider in the UK to offer left-handed ATMs, starting from April 2015.
New EU discrimination regulations require banks and other account providers to do more to accommodate minorities, including left-handed people.
Latest estimates suggest that 11% of people in the UK are left-handed, meaning around 5.5 million adults will benefit.
However, the first left-handed cash machine won't be available for use until 2015, due to the difficult engineering task of reversing the machinery. It's thought that the job may be outsourced to Germany, as none of the UK's ATM manufacturers currently have the technology to build left-handed machines.
Ian Williams of thinkmoney said: "We are always looking for ways to help our customers, and we realised that left-handed people get a raw deal when it comes to withdrawing cash.
"Our right-handed customers can still use the cash machines, either by switching hands or simply stepping to the left when entering their card."