Space Solutions, which has its registered office in Aberdeen plus further sites in Livingston, Edinburgh, Glasgow and Dundee, said it had seen a growing demand from clients in England.
Although it already handles UK-wide briefs for some clients, the acquisition of CMA is expected to improve capacity to serve a wider geographic area.
Steve Judge, managing director of Space Solutions, said: "We have been considering the move into England for some time, as the number of UK-wide contracts and jobs specifically in London increased.
"We are pleased to add such an established business to the group. With a solid reputation for quality, CMA is the perfect fit and we look forward to continue to service its strong customer base."
CMA, best known as a pioneer of open plan offices in the 1980s, has a wide client list across the corporate and public sector.
It has recently won a trio of projects for engineering firm Amec plus office fit outs for The Linde Group and a government department in London.
The most recent annual accounts for Space Solutions, covering the 12 months to June 2011, show it reported a 13.5% rise in pre-tax profits to £336,052 on the back of a near 22% growth in turnover to £19.6m.