Abercrombie Gemmell, formed 23 years ago by husband and wife Colin and Christine Abercrombie, turns over £1 million from services such as tax advice, audits and wealth planning.
Its 12 staff will transfer to French Duncan's new office close to the Hydro in Glasgow, with Mr Abercrombie joining as a partner and Mrs Abercrombie as a consultant for a certain period.
However, the Abercrombie Gemmell name will go.
French Duncan said its turnover will rise to £10.5 million following the deal.
The value of the acquisition was not disclosed but it comes after the firm took on the tax consultancy team from Chiene and Tait earlier this year. That came around 12 months after French Duncan, which employs 200 staff across offices in Glasgow, Edinburgh, Stirling, Hamilton, Dumbarton and Kirkintilloch, merged with Stirling-based Macfarlane Gray.
Graeme Finnie, managing partner at French Duncan, said the Glasgow-based firm remains "keen to grow" and declared he detects opportunities for that within the Scottish accountancy sector.
Asked what had attracted French Duncan to Abercrombie Gemmell, he highlighted the clients it held and its reputation in the industry while suggesting that Mr Abercrombie had "punched above his weight" during his years with the firm.
Mr Finnie said: "When the conversation came up between the two of us, Colin really wanted to move on to a bigger playing field. He felt he had taken Abercrombie a long way, but felt now was the time to merge with somebody else that would give him and his clients access to a greater breadth of services. That was his logic. From a personal perspective, Colin is probably one of the best business developers and one of the most commercial accountants in practice I have come across."
Mr Finnie said he was not interested in competing with rivals on price but wants to beat them on the quality of advice the firm offers across its market sectors. This extends to areas such as recruitment and human resources as well as accounts and tax advice.
Mr Finnie explained: "It's clichéd but it's true - we want to be the adviser of first choice. We want to be the adviser that, if you've got a problem or you want to bounce something off, you pick up the phone to.
"And Colin, I would say, is already there with that with his clients, as we are. For his clients he is very much the go-to guy.
"He is their most trusted adviser and that's really why there was a really clear, cultural fit with us."
Mr Abercrombie said: "In order to continue to offer the commitment to the delivery of a personal, high-quality, proactive service, the time is right for Abercrombie Gemmell to merge our operations with that of like-minded, progressive French Duncan.
"Myself and my colleagues are totally committed to the future of the newly-merged operation and are genuinely excited about the service quality enhancements that this merger will offer our existing clients."
Mr Finnie said the business plan for French Duncan targets growth both organically and through further acquisitions, having made several strategic appointments at senior level since he became managing partner three years ago.
Some of these recruits have come from "big four" accountancy firms.
Mr Finnie added: "Macfarlane Gray has gone magnificently well for all concerned, and I have no doubt that Abercrombie Gemmell will go the same way.
"We are not on the cusp of doing anything in the next six months, but certainly I would envisage that within a year we will hopefully have something else on the agenda by way of acquisition.
"But it's got to be a good strategic and cultural fit."