The announcement came as fellow part-nationalised institution Lloyds Banking Group, owner of Bank of Scotland, sent out documents to shareholders asking them to back a 200% bonus for top executives.
Mr Stevenson was born in the UK but raised in New Zealand and worked for Credit Suisse in both countries.
RBS chief executive Ross McEwan, who is also a New Zealander, said "Ewen has spent many years working with the world's leading banks. In recent years he has been a trusted adviser to both governments and company boards on the steps needed to restore confidence in financial institutions following the crisis.
"At RBS we are determined to re-earn the trust of our customers and our continued financial health is central to that task. Ewen shares our vision for building a great customer bank."
Mr Stevenson is currently co-head of Europe, Middle East and Africa Investment Banking and of Credit Suisse's global financial institutions group, investment banking division. He has worked for the bank for 25 years.
How big a pay package 81% state-owned RBS have had to offer Mr Stevenson to secure his services will be revealed when he joins the Edinburgh-based bank on May 19. RBS will also compensate him for share incentive awards lost when he quits Credit Suisse.
RBS said that Mr Stevenson has extensive management and restructuring experience. In 2008 and 2009 he was a member of the Credit Suisse team advising HM Treasury on its bail-out of RBS and Lloyds and the restructuring of Northern Rock.
Gary Greenwood, analyst at Shore Capital, said: "We view this as positive news as it removes uncertainty around the position and should therefore enhance investor confidence in the company's ability to deliver on its strategic plan.
"The fact that it is an external appointment also helps to deflect concerns that the company is struggling to attract talent owing to its relatively onerous ownership and governance situation, we think."
Lloyds yesterday sent a circular to investors ahead of its annual investor meeting in Edinburgh on May 15, asking them to approve bonuses of up to 200% of basic pay for its estimated 400 senior code staff. It needs investor approval to exceed a European Union bonus cap of 100% of salary.