Rose, who will receive a basic salary of £1.1 million at the Edinburgh-based lender, which remains part owned by the taxpayer, was the heavy favourite to succeed Ross McEwan when he departs from the group on 31 October.
She is currently the bank’s chief executive for its commercial and private banking arm, as well as deputy chief executive of Natwest Holdings.
Rose will take up the top post on 1 November after an “orderly handover” has taken place.
The appointment will make RBS the only company in the benchmark FTSE 100 index with women in its top two executive positions, joining chief financial officer Katie Murray.
Rose said: “It is a huge honour to have been appointed as the new CEO of RBS and I am looking forward to getting started. As one of the oldest and most important financial institutions in the UK, we have a key role to play in supporting the economy and championing the potential that exists across the country.
“Under Ross’ leadership, RBS has undergone a significant transformation and, as part of his leadership team, I am extremely proud of all we have accomplished, and I would like to thank him for the support he has given me over the last six years.
“Maintaining the safety and soundness of this bank will continue to underpin everything we do, as will our commitment to our customers and to delivering steady returns for our shareholders.
“This is an exciting time as we enter a new chapter for this bank. Our industry is facing a series of challenges; from the ongoing economic and political uncertainty to shifts in the behaviour and expectations of our customers, driven by rapid advances in technology.
“It will be my priority to make sure we are ready to meet these challenges and build the best bank for families, businesses and communities.
“We will be driven with real purpose in our work to help achieve the goals and potential of our customers and be there for them at key moments in their lives.”
RBS chairman Howard Davies added: “I am delighted that we have appointed Alison as our new CEO. She brings extensive experience and a track record of success from her previous roles at the bank.
“Following a rigorous internal and external process, I am confident that we have appointed the best person for the job.
“I’d like to take this opportunity to thank Ross, on behalf of the board, for his leadership and commitment during his time as CEO and wish him the very best for the future.
“Ross leaves a strong platform for his successor; a bank that has refocused on its core markets in the UK and Ireland and resolved all its major legacy issues, while returning to profitability and paying dividends.”
Rose’s pay package includes a base salary of £1.1m, a fixed share allowance set at 100 per cent of salary and standard benefit funding of £26,250 per annum.
RBS said remuneration had been set “at a level that reflects the fact that the current CEO’s salary has been unchanged since his appointment in 2013”. Pension funding has been set at 10 per cent of salary – in line with the pension rate applicable to the wider RBS workforce.
Variable pay will be delivered entirely in shares as long-term incentive awards, with a maximum award of 175 per cent of salary. Rose will be required to build up and maintain a minimum shareholding equal to 400 per cent of salary.
The bank added: “Alison’s remuneration package continues to represent a restrained pay position in terms of comparable roles.”
McEwan was on a basic salary of £1m. No payment will be made in lieu of notice.
Shore Capital analyst Gary Greenwood said: “Following a somewhat protracted process, RBS has finally announced the appointment of Alison Rose as an executive director and the group’s new chief executive officer.
“Alison was widely viewed as the leading candidate for the role and so her appointment should not really come as a surprise.”