Price could reach £7.4m, depending on future performance.
Alpha is a retail design and fit-out specialist based in Paris servicing international retail companies.
ISG already has offices in Paris, Amsterdam, Frankfurt, Geneva, Milan and Moscow. These operations will now be merged into Alpha and the principal vendor, André Bernstein, who has 30 years of retail experience, becomes managing director of the combined mainland Europe retail fit-out business.
Alpha has delivered numerous projects for clients including Apple, Louis Vuitton, Gucci, Tiffany & Co. and Patek Phillipe. In addition to its core French market, Alpha has also delivered projects for clients in Italy and Switzerland.
Alpha's turnover for the year ended 31 October 2010 was £6.5m and generated a contribution of approximately £200,000. Alpha has net assets of approximately £400,000 at completion and employs 20 people.
ISG said that the acquisition gave it a design and fit-out turnkey solution for its international retail customers in France and Italy, and also strengthened its management team.
At completion £1.5m will be paid in cash by ISG. A maximum further consideration of approximately £5.9m is deferred and payable after the two financial years to 30 June 2013, conditional on the business meeting average profit before tax targets for the two years. The deferred consideration will be settled 80% in cash and the balance in new ISG ordinary shares.
ISG chief executive David Lawther said: "The Alpha acquisition is a key part of our continuing international expansion strategy and we are delighted to have acquired this capability within ISG. The acquisition will widen our international retail client base and provide a broader retail service offering to our clients in Europe."