The takeover is part of Thomas Miller's wider growth strategy to build it into a leading investment management business, the company said as it announced the move this morning.
Broadstone, which has offices in Glasgow, Southampton, Birmingham, Chelmsford and London, provides wealth management services to private clients, pension funds, charities and companies and manages and advises on approximately £400 million of assets. It is part of Broadstone Pensions and Investments.
Thomas Miller, which operates out of London, Edinburgh and the Isle of Man provides services to institutions and private clients both on and offshore, overseeing £2.4bn of funds under management.

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After the acquisition Thomas Miller will manage and advise on about £2.8bn of assets with approximately 90 staff across 7 locations.
Broadstone's managing director, private clients, Matthew Phillips, will take responsibility for Thomas Miller Investment's wealth management operation in the UK.
Mr Phillips said: "The additional expertise and resources we will gain as part of Thomas Miller Investment will deliver long term value to our clients.
"Thomas Miller Investment's culture and heritage are complementary to ours and we have been very impressed with the calibre and depth of their investment team.
"We believe this strategic decision is in the best interests of our clients, staff and wider stakeholders."
Mike Balfour, chief executive of Thomas Miller Investment, said: "The team at Broadstone share our philosophy and culture of providing a highly professional service for clients.
"They will be a valuable addition to our investment capability and provide a national wealth management offering in addition to our other offices.
"This is a clear demonstration of our ambition in the provision of private client wealth management."
The acquisition is subject to FCA approval.