The Cambridge Crescent branch closure on August 8 is among a list of closures announced by the group.
In a statement this week, RBS said customers had changed in the way they did their banking, and technology now enabled customers to use NatWest branches for everyday banking.
RBS said that the number of regular weekly customers at the Harrogate branch was below 50.
The statement said: “The way people bank with us has changed radically over the last few years. Since 2014, branch transactions across the Royal Bank of Scotland in England and Wales fallen by 30 per cent.
“During the same period, there has been a 53 per cent increase in the number of customers using mobile banking and mobile transaction have increased by 74 per cent.
“Since 2012 we have seen the way in which people use Harrogate branch change, with 75 per cent of customers already banking in other ways locally.
“Transactions at Harrogate have reduced by 53 per cent since 2012, with only 46 customers now visiting the branch on a regular weekly basis.”
RBS in England and Wales had been due to be divested and launched as a separate challenger bank, under the name, Williams and Glyn..But plans had changed.
As a result, RBS had held an overall branch network strategy review.
RBS says that this took into consideration that there were two branch networks close to each other - NatWest and RBS in England and Wales.
Alongside technology enabling customers to use Natwest branches as they currently use RBS, they will be also be able to seek support from staff there.In the statement RBS also stated it would contact vulnerable customers to let them know about the changes.
Support will be offered through a new taskforce, RBS TechXperts, they say. This will be available until the branch closes.