It will relaunch the brand in March with activity kicking off in Scotland, focusing on urban areas and linking the brand with hip hop music.
It will double the £1.5m it invested in promotional activity last year.
Miller Brands UK has taken control of the marketing and distribution of SABMiller's lager brands from Scottish & Newcastle, which had been promoting them on behalf of SABMiller since SAB acquired Miller in 2002.
Miller Brands UK will also oversee SABMiller brands including Peroni Nastro Azzurro, Pilsner Urquell and Castle Lager.
SABMiller, which operates in more than 60 markets worldwide, created Miller Brands UK last July to focus attention on the UK market. The company has been given a £30m promotional budget to raise the profile of its premium lager brands.
John-Pierre van Lin, previously managing director UK and Ireland for Miller Brewing International, has been appointed top marketer at the firm.
While Miller Genuine Draft has a premium positioning in the UK, in the US it targets the mass market.