Turris has £65m in assets under advice and provides Financial Planning and wealth management advice.
It was established in 2003 and has five staff based in Glasgow who will be retained by Mattioli Woods.
Turris was founded by managing director and Chartered Financial Planner Brian Steeples, FCSI, FPFS, ACII who was the first President of professional body the Personal Finance Society.
Turris generated £450,000 in revenue and pre-tax profit of £150,000 in the year ended 30 September. Mattioli says it expects the deal to be earnings enhancing in the first full year of ownership.
The deal comprises initial cash of £800,000 and deferred consideration of up to £800,000 payable in cash on the first and second anniversaries of completion, subject to financial targets being met based on recurring revenue.
Ian Mattioli, chief executive of Mattioli Woods, said: "We put a great deal of thought into any acquisition that we consider, as it is so important to make sure it is a good cultural fit.
“We are very pleased that Brian and his team are joining Mattioli Woods. It is an important acquisition for us, as we have been looking to expand our operations in Scotland and opportunities to acquire such a well-respected business don't come along every day."
Brian Steeples added: "The additional resources and support available as part of Mattioli Woods will benefit clients and staff and we very much look forward to this exciting new phase.”