The agency won the account without a pitch, and will now be responsible for driving sales across the company's range of brands.
Rapp will work on both acquisition and retention activity, using a range of CRM and eCRM campaigns.
Rapp's appointment comes as DSG looks to step up its customer retention activity in response to the planned arrival in the UK of the American electrical giant Best Buy.
The company has recently announced that it is looking for a new head of CRM.
The retailer is also set to refurbish more than 100 stores, and has recently relaunched its Currys brand.
DSG currently works with a number of agencies across its range of brands, including M&C Saatchi on its advertising account.
The company is also understood to be seeking an agency to handle an upcoming digital project. A number of agencies have been contacted directly by the company with an initial request for information.