RBS said the decision was the result of a "dramatic shift" in how customers interact with banks, the BBC reports.
Branch transactions had fallen 43% since 2010, it said – while online and mobile transactions had increased fivefold.
The move will affect about 770 staff, with many of these jobs lost – but some workers will be redeployed. 128 of the branches being closed are NatWest, and 30 RBS.
An RBS spokesman said: "We interact with our customers over 20 times more through digital channels than physical ones. 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."