Alexander Sloan said that 42-year-old Philip Morrice, who has been with the firm since 1993 and is head of its internal audit department, has taken on the top role.
He replaces Ewen Scott, 52, who will remain with the firm and go back to running its taxation practice.
Sandy Mowat was the previous youngest to take the role when he started to lead the firm at the age of 45 in 1995.
Mr Morrice, the Scottish member of the global business law forum run by the Association of Chartered Certified Accountants, said it was a "great honour" to be chosen to lead the business in the run up to its 150th anniversary in 2017. He indicated that he will be looking at introducing ways of working with new technology and re-positioning the firm's brand over the coming months.
Alexander Sloan, which has offices in Edinburgh and Glasgow, can trace its roots to 1867.
Andy McBean, senior partner at the firm, said: "Alexander Sloan is a very special firm and its direction could not be in better hands that those of Philip.
"His drive and enthusiasm as well as his keen managerial skills make him the ideal person to take the firm forward."