The RBS Shareholder Action Group will take the 82 pence per share offer, which was raised from 43 pence per share, after failing to secure a better one in negotiations with RBS CEO Ross McEwan last week.
Tuesday's decision brings close to a long-running dispute, which saw 27,000 investors allege they were misled about the financial position of the bank when it launched a £12 billion rights issue in April 2008, six months before RBS collapsed into the arms of the British government as the financial crisis escalated and a pile of mortgage loans bit deeper into RBS' capital buffer.
A majority of investors had already accepted settlement proposals although a small group of around 2,000 had held out for a better deal and, on Tuesday morning, it was reported that the remaining litigants had secured the funding necessary for them to see out a trial.
RBS stock slipped during early trading and remained in the red at 13:00 BST, down 1.7% for the session, changing hands at 255 pence. The stock is up by 15% for the year to date while the Stoxx Europe 600 Banks index shed 0.47% Tuesday.
If the lawsuit had progressed to a trial, it may have meant former executives being called to testify and likely revealing previously undisclosed details about how the bank's executive team responded to the financial crisis.
The U.K. government still owns more than 70% of RBS. The lender reported its ninth straight year of losses in February, after booking multiple provisions for anticipated settlements of other legal cases.
The failed separation of Williams & Glyn, ordered by the European Commission, meant a one-time charge. This added to the cost of a $3.8 billion to cover an anticipated residential mortgage-backed securities settlement with the Department of Justice.
The lender has made substantial progress, however, in slimming itself down and refocusing on core domestic markets over the years.