Epoch said it was "with great pride" that it could announce the sale, which its said “marks a real milestone in our journey, and that of our clients”.
Epoch revealed its clients were being communicated with individually about the change.
A company statement read: “Epoch has built a solid reputation for giving its clients sound Financial Planning advice and occupying the role of ‘trusted adviser’.
“In Brewin Dolphin, we believe we have found a firm which not only has the financial strength to allow us to grow and develop our client offering, but also shares many of the same ideals we hold high.
“In this regard, we believe that our clients and those who have built up a relationship with us over the last nine years should share in our pride."
Epoch will become the Bath branch of Brewin Dolphin “with little change”.
The firm said its clients clients would “still receive high quality Financial Planning advice but will also enjoy enhanced services and an improved proposition as a result of us being part of a larger firm”.
The firm vowed to retain its entire team, operating from the same office.
Epoch’s managing partner, Barry Newbury, said: “This is a seminal moment in Epoch’s journey and we are delighted to be joining Brewin Dolphin for the next chapter of our story.
“We have worked extremely hard to ensure our clients, staff and other stakeholders benefit from this deal and we believe we have achieved this goal. We look forward to the future with
Brewin Dolphin and are excited about the opportunities this will bring for our clients.”
Nick Fitzgerald, managing director of Financial Planning at Brewin Dolphin, said: “What we’re seeing across the country is pent up demand for good financial advice, especially in these uncertain times.
“Barry and his team have built Epoch Wealth Management into a successful business trusted by their clients.
“We’re so pleased that their advice-led team are joining us to continue their growth journey, and as one of the UK’s largest wealth managers we’re able to provide them with the resources they need to provide their excellent advice to more clients and to grow.”