Topshop will task Cooke with taking the brand international as Green seeks to increase Topshop’s presence in America, alongside examining an entry into continental Europe and China.
It is understood Cooke will join in September and will report into Topshop managing director Mary Homer and will also work closely with Sir Philip Green, the boss of Topshop owner Arcadia.
During his five and a half years at Burberry, the brand managed to revitalise its image and carve out a name for itself in the digital space.
Green said: "With Topshop’s ambitious plans both at home and overseas for digital marketing and social media in particular, this is a very exciting time to bring someone of Justin’s calibre on board.
"I am an admirer of how Burberry has been an innovator in many areas, so Justin’s experience from his time there will add a new dynamic to the team, and we are delighted that he is joining us."
Topshop traditionally spends a very small amount on marketing in the UK. Arcadia, the parent company of BHS, Topshop and Topman, is currently reviewing its £4m media planning and buying account, which is worth £4m.
The bulk of Arcadia’s spend is focused on BHS, which accounts for around £3.5m, while Topshop and Topman together spend around £600,000, according to figures from Nielsen.
Cooke's departure from Burberry will not affect the brand’s marketing arrangements because its marketing is handled by chief marketing officer Sarah Manley.
Cooke’s other experience includes work at high-end fashion brands including Stella McCartney and Gucci.
The last person to occupy the marketing director role at Topshop, Andrew Glenn, moved to New Zealand in late 2010.
Follow Matthew Chapman at @mattchapmanUK