The sum paid for Alphastrut, which makes aluminium support structures, has not been disclosed.
It comes two years after Murray International Holdings, which is chaired by Sir David, sold Murray Metals to members of its management and his own Murray Capital investment vehicle.
Graeme Hill, chief executive of Murray Metals, which previously held the global licensing agreement for Alphastrut, said: "This is a key strategic acquisition.
"It diversifies further not only the range of our offering in speciality metals, but broadens and strengthens our national and international reach."
The Alphastrut product, an alternative to traditional steel support systems, has been installed in developments including on platforms owned by BP on the Clair Ridge, west of Shetland, where it was incorporated in flooring and cable-management support systems, and was used in the living quarters of the oil giant's Valhall oil field platform off the coast of Norway.
Mr Hill, who becomes chairman of Alphastrut, added: "After the last few years of consolidation, in the face of difficult times for the construction and other associated industries, Murray Metals is again driving forward in both existing and new markets."
He said the business will seek further acquisitions.
Andy Munro, product creator and co-founder of North Lanarkshire-based Alphastrut, said: "Alphastrut has worked closely with Murray Metals over the past two years, under a global licensing agreement.
"We are delighted now to pass on the baton to them as they have the resources, experience and reach to exploit Alphastrut's exceptional international and cross-sector potential."
He will join the 200-strong workforce at Manchester-based Murray Metals as technical director.
Murray Metals director Craig McDermid, who is also investment director of Murray Capital, said: "It is exactly the type of investment opportunity - one that offers outstanding international sales potential - that symbolises Murray Capital's ambitious, forward-looking growth strategy."
The move comes just weeks after trustees of Murray International's pension scheme raised worries about the group's "worsening financial position".
Murray Metals encompasses Murray Plate Group, which has sites including Edinburgh, Hillfoot Steel, which is based in Sheffield, and Multi Metals, with sites in Sheffield and Glasgow.