The appointment comes as Asda bolsters its use of local marketing, more than doubling its £5m budget to help improve sales.
The business will be managed at Brilliant by a five-strong account team, which will be responsible for developing regional advertising campaigns to generate sales across Asda's 280 stores.
Chris Pilling, Asda's marketing director, said: "We're very excited about the new partnership and Brilliant seem to be the perfect fit for us."
In July, Asda's new chief executive Andy Bond slashed jobs across its network. It also made a number of additions to its board, which led to the promotion of trading and marketing director Angela Spindler to the newly created post of customer and strategy director.
The move comes after Asda brought in auditors to examine its use of regional marketing.
Asda's sales are improving. It reversed its recent downward sales trend, according to the latest TNS Grocery survey. The supermarket had a 16.6% share for the 12 weeks to July 17, a year-on-year rise of one percentage point.
Asda's advertising is handled by Publicis and the current campaign features Sharon Osbourne.
Brilliant was founded in 1999 following the merger of DMS and Media Lane. The agency's headquarters is based in Leeds and it also has an office in Manchester. Other clients include Subaru, Morphy Richards, and DVLA.
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