Brown, former head of CSM Sport & Entertainment, had been linked to the position after Ron Dennis was forced out as chairman and chief executive of McLaren last week.
"In this senior role, Zak's appointment will be a significant part of a restructuring programme that will align the Group's commercial and strategic operations relating to achieving success in Formula 1," McLaren said in a statement.
Brown added: "Having worked closely with McLaren for many years, I've been struck by the talent and ambition of the entire workforce, and I very much look forward to complementing the business' many existing strengths, and building on them to drive future success in everything we do.
"...I'll be able to combine my absolute passion with my unparalleled area of expertise - respectively motorsport and marketing - while ensuring that the two stay totally aligned."
McLaren said Brown and CEO Jonathan Neale, reporting directly to the Group's Executive Committee, would jointly lead the businesses as part of the first step in the transition to a new and strengthened organisational structure.
McLaren, whose team last won a race in 2012, are currently looking for a new Group Chief Executive Officer.
