Cooke, who has worked at Tesco for 21 years, most recently as a category manager for books, newspapers and magazines, takes up his new role on 28 September. He will be responsible for newspaper and magazine accounts and allocations, regional press, retail relationships and contact centres.
He replaces David McIntosh, who moves up to the role of MD, replacing Ellis Watson who last month announced he was leaving the business to join the main board of transport company FirstGroup.
"I'm delighted to welcome David to the business," McIntosh said. "He will bring strong industry relationships and commercial acumen to the role."
As part of the management reshuffle, wholesale director Tom Boyle, who is credited with successfully concluding a number of recent substantial contract wins for Menzies at the expense of Dawson News, has decided to step down from his role on 31 July.
Head of branch operations Alex Mitchell has been promoted to operations director, with responsibility for the wholesaler's branch network.
HR manager Christina Mellon moves up to the role of HR director. Both will take up their new roles on 1 August.