Sharpe, who has 35 years of senior executive and board experience, has been chief executive of West Bromwich Building Society, Portman Building Society and Bank of Ireland in the UK.
He said: “I am joining Al Rayan Bank at a very exciting time.
“The bank is strongly committed to achieving ambitious growth targets and I look forward to steering the bank along a path to even greater success.”
In early 2014 the bank was acquired by Masraf Al Rayan, while it received full shareholder approval to change its name and brand in December 2014.
Sharpe's expertise spans strategy and planning, corporate governance, risk management, audit and control, financial services regulation and M&A activity.
Sultan Choudhury, chief executive of Al Rayan Bank, said: “Robert brings a wealth of board experience and his expertise of the retail and commercial banking sector in the UK will play a significant role in helping the Bank to achieve the strong balance sheet growth it is aiming for.”
