RBS said in a statement that Stevenson, who is currently Credit Suisse's London-based co-head of investment banking for Europe, Middle East and Africa, will join on May 19th.
Stevenson, 47, was a senior member of the Credit Suisse team advising the British government in 2008 and 2009 on the recapitalizations of both RBS and Lloyds Banking Group.
"Ewen has spent many years working with the world's leading banks," added RBS chief executive Ross McEwan in the statement.
"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."
Edinburgh-based RBS was rescued with £45.5 billion of taxpayers' cash at the height of the 2008 global financial crisis, making it the world's biggest-ever banking bailout.
The government still owns 81 percent of the troubled lender.