Lack is leaving to join a so far unnamed investment fund.
He has previously held roles at Coutts, Royal Bank of Scotland, Morgan Stanley and UBS Investment Bank.
Lack is still in position at present, with an exact leaving date yet to be confirmed by the company. The process of recruiting his replacement is underway.
A Brewin Dolphin spokesperson said: “Tom Lack has resigned to pursue another opportunity at an investment fund. He remains at the firm. He has built a strong and resilient team, and we anticipate announcing his replacement shortly. He leaves with our best wishes and thanks for delivering the changes and management team that will enable us to continue to develop the firm.”