Rose is also the first woman to be appointed to lead one of the UK’s major banks.
She has been appointed additionally as executive director and chief executive on the boards of NatWest Holdings, Royal Bank of Scotland, National Westminster Bank and Ulster Bank.
“As one of the oldest and most important financial institutions in the country, we have an important role to play in supporting the economy and championing the potential that exists across the country,” Rose said.
“This is an exciting time as we enter a new chapter for the bank. Our industry faces a series of challenges from ongoing economic and political uncertainty to shifts in the behaviour and expectations of customers driven by technology.
“My challenge will be to ensure we are ready to meet these challenges and to build the best bank for families, businesses and communities,” she added.
Rose also noted that RBS had undergone a significant transformation under McEwan and, she was proud to be part of his team and what it had accomplished.
RBS chairman Howard Davies said: “I am confident that we have appointed the best person for the job following a rigorous internal and external process.
“I’d like to thank Ross on behalf of the board for his leadership and commitment,” Davies added.
Rose steps up from her current position of deputy chief executive and chief executive, commercial and private finance.
She is a non-executive director of Great Portland Estates and a member of the board of Coutts Charitable Foundation.