Knaresborough and Tadcaster will be among the areas hit as more than 150 Royal Bank of Scotland and NatWest branches are set to close, with hundreds of job losses.
The decision will affect 30 RBS and 128 NatWest branches and hit around 470 jobs.
The news means that NatWest branches in both Knaresborough and Tadcaster will close permanently in October this year.
A spokesperson for the company said: "The way people choose to bank with us has changed radically over the last few years. Between 2010 and 2015, mobile and online transactions have increased by over 400% and mobile transactions alone have increased by 1,350%.
"We are communicating with our customers affected by the closure and proactively contacting vulnerable and regular branch customers. We have listened closely to feedback from local communities and have extended the time between announcing our decision and the branch closure to six months. This has been done in order to ensure our customers have time to consider the right banking options for them.
"We know that not all of our customers are comfortable and familiar with using online or mobile banking, so we have created a new specialist taskforce of TechXperts who will be dedicated to supporting our customers with training and support with digital skills."
Since 2011 the company said it had seen the number of in-branch transactions fall by 44 per cent in Knaresborough and by 20 per cent in Tadcaster.
By contrast, in the same period customers choosing digital banking options have increased by 61.7 per cent in Knaresborough and by 62 per cent in Tadcaster.
The Knaresborough branch will close on October 3 2017 while Tadcaster customers will have until October 5.
Some 770 jobs across the UK will be affected, although 300 of those will be moved to other roles.
A spokesperson said: "We are following the Access to Banking protocol and we have made the decision after careful consideration of a wide range of factors, including regular branch usage and the alternative ways our customers can bank with us."
The nearest branch for NatWest customers in Tadcaster will now be more than nine miles away in Wetherby and for Knaresborough Natwest customers it will be Harrogate.
RBS said customers will still be able to bank through online, mobile and telephone services and services will also be available through the Post Office.