Parker has been at DDB London for the past seven years and has partnered the copywriter Jo Wenley.
The duo were behind the Harvey Nichols "boxing ring" campaign, which scooped a bronze award at Cannes this year. Parker has also worked on The Guardian, and was behind the Volkswagen "life in a day" ad.
Parker joined DDB in 1999 on a creative placement with the copywriter Patrick McClelland. The pair were behind Harvey Nichols' "heaven and earth" poster campaign.
Jeremy Craigen, the executive creative director at DDB London, said: "Promoting Grant to head of art was an instant choice. He has always deputised when Justin was away. He continues the tradition of great heads of art at the agency and importantly he had Justin's blessing."
Last week, Paul Hammersley, the founder of TRBR, raided his former agency, appointing Tindall as a creative partner and DDB's head of account management, Karen Fisher, as its managing director.