The group, which warned that current trading "remains relatively slow", said Parry will conduct a thorough review of the business over the next few months, once he joins on July 2.
The business comprises UK marketing communications, including CMW and Dynamo; UK marketing services, including Coutts Retail Communications; international advertising and intelligence, including The Gate Worldwide and German agency SEA; and online advertising and technology, including TwentySix.
It admitted it had poorly executed its strategy of integrating the various businesses it has acquired over the past four years, particularly in its UK marketing services division, which includes Coutts Retail Communications.
Although Media Square's revenue jumped 41% over the year ended February 28 2007, its underlying pre-tax profit dropped 14% to £4.5m. However, exceptional costs and the non-cash writedown of goodwill on disposals took it into a loss.
During the year it sold Karen Earl Sponsorship and digital agency Tangozebra at a profit, and direct marketing agency SBGFinex at a loss.
Parry's arrival at Media Square bumps up his impressive tally of media and marketing roles. He is currently chairman of YouGov, Johnston Press, Future and Mobile Streams, as well as Shakespeare's Globe Trust.
He has previously worked for McKinsey, WCRS and Aegis and was chairman and CEO of Clear Channel International.
He said: "I am delighted to be joining Media Square at a very interesting time in its history. The integration of the various businesses acquired over the past few years has been challenging and complex but the company is now stabilised around a strong group of well-focused operations."
Middleton will act as a consultant to the business during a handover period, and has left the company with the gratitude of the board for his hard work -- in taking Media Square from £3m in billings to more than £200m in billings, over five years.
Media Square's share price was unchanged in early trading, at 11.75p. Its lowest point in the past 12 months was 10p at the end of March and its highest was 24.5p in July last year.