Clark McKay employs more than 75 staff and its client list includes Renault, Porsche, Cancer Research UK, Weight Watchers, Index, GNER and Transport for London.
The acquisition has increased Media Square's client base to more than 250 and doubled the size of its marketing communications business.
Clark McKay will continue to work as a standalone agency and will retain its brand name and management structure. Chairman and co-founder Jonathan Clark and managing director and co-founder Janet McKay will continue to run the agency from its offices in Marylebone in central London.
According to Clark: "With Media Square's support and commitment we can grow the Clark McKay Walpole brand at a much faster pace than would have been possible by using internal resources alone."
The acquisition of Clark McKay is Media Square's 10th acquisition in the past 20 months and the fourth this year. The move takes the group's employee numbers to 320.
Last year it bought Banc, the agency set up by former BT advertising director Robert Bean.
Jenny Middleton, chief executive at Media Square, said: "Clark McKay's focus on excellent client service and a high quality end product combined with the profitable development of their business means that it will be a very valuable addition to our marketing communications offer."
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