He will be replaced by David Nicol, who joined the board as a non-executive director in March 2012, and the firm said Mr Matheson would ensure a smooth handover.
Mr Nicol previously worked at Morgan Stanley and served on the Morgan Stanley board until 2010. He has also worked as a board member at the Chartered Institute of Securities since 2002.
Stephen Ford was appointed as executive director of investment management while Henry Algeo, Ben Speke and Sarah Soar all stepped down.
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Chairman Simon Miller said: "On behalf of all our employees and shareholders I want to thank Jamie for his dedication to Brewin Dolphin over the years. His contribution has been immense and his strong leadership has built Brewin Dolphin into one of the UK's leading private client wealth managers, based on a total focus on client service which is core to how we will continue to develop the business."
Mr Matheson said: "Having led Brewin Dolphin through a significant period of growth and steered the business through the changes brought about by the RDR, I believe it is time to hand over the reins. I am proud of what we have achieved and believe that the Company is well structured to build on its enviable position.
"I have enjoyed my many years at Brewin Dolphin and while the decision to step down is never easy, the time is right for me and the business. I am confident that I leave Brewin Dolphin on a sure footing and with bright prospects."

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