The branches in Biggar, South Lanarkshire, and Castlebay on Barra in the Western Isles will not be closed due to independent reviewers citing “exceptional circumstances”.
However, the closure of eight branches out of the 10 under review has now been confirmed, in addition to 52 previously announced.
Branches in Beauly, Tongue, Kyle, Melrose, Inveraray, Comrie, Douglas and Gretna will all shut on dates yet to be determined.
The announcement follows the recommendations of an independent review into the 10-closure threatened branches the bank commissioned from accountancy and business advisory firm Johnston Carmichael.
The 10 branches were chosen as they were mostly all the last branch in town and more than nine miles from the nearest alternative RBS branch.
For the Barra branch, the decision to keep it open is partly due to concern that the mobile bank may have been unable to reliably reach island in bad weather.
The Biggar branch was given a reprieve due to local demand and the nearest RBS branch being 13 miles away in Lanark.
The reviewers have also recommended additional steps are taken to improve the quality and accessibility of alternative banking facilities for six of the closing branches such as not closing the attached bank machines and expanding mobile bank provision.
RBS managing director of personal banking Simon Watson said: “Johnston Carmichael has judged that there are exceptional circumstances in Biggar and Barra, and has recommended that these branches remain open - so they will.
“We also note the further recommendations for enhancements that can be made in six of the branch locations and can confirm we will be accepting these recommendations in full.
“The report highlights the difficult nature of branch closure decisions. We know branches are important to many communities, but equally we know that fewer and fewer people are using them as more people bank online.
“In every case of a branch closing we are committed to providing the best possible range of banking alternatives, including mobile branches, banking in the local post office, community bankers and remote services such as telephone banking.”
He said there would be no further branch reviews until at least 2020.
Sandy Manson, chief executive of Johnston Carmichael, said: “We understand there will be considerable disappointment in those communities where we have recommended that a branch should close.
“However, in most cases where we have recommended that a branch close, we have also suggested additional steps which we believe the bank should take to enhance the quality and accessibility of the alternative banking facilities available.
“We recognise the importance of local banking services being available to these communities and we have therefore carefully set out our rationale for reaching each recommendation on a branch-by-branch basis.”