The decision will affect 30 RBS and 128 NatWest branches and hit around 470 jobs.
The Yorkshire branches closing include Adel in Leeds. Bingley, Bradford city centre , Settle, Haxby York, Otley, Selby, Knaresborough and Tadcaster.
The company said it had considered branch usage and the alternative ways customers can bank, adding: “We have seen a dramatic shift in the way our customers are choosing to bank, with more using mobile and online over traditional branch counters.
“Simple transactions undertaken in branch at NatWest and Royal Bank of Scotland have fallen by 43% since 2010, while online and mobile transactions have increased by more than 400%.”
Around 770 staff will be affected by the closures, but 300 will be moved to other jobs.
Two new roles have been created - community banker and NatWest or Royal Bank of Scotland TechXpert.
Community bankers will serve the local area, with a particular focus on rural communities, providing customers with personal assistance and support.
There will be 50 community bankers in post across the UK by the end of 2017.
The specialist taskforce of NatWest and Royal Bank of Scotland TechXperts will support customers with training and support with digital skills.
An RBS spokesman said: “Many more customers are choosing to do their banking using mobile and online services over traditional branch counters.
“We interact with our customers over 20 times more through digital channels than physical ones. We have 4.2 million personal mobile users, up by over two million since 2014. As customers change the way they bank with us, we must change the way we serve them.
“The role of the branch is fast moving to a centre for advice, away from basic transactions. While the branch will still be a core part of our offering to customers, inevitably some branches will have to close.”