He replaces Alex Anson, who has moved to Switzerland to take up the role of European buying director for airport shop operator Nuance.
Anson had made a "fantastic" contribution to the business, said Thresher Group chief executive Roger Whiteside, who added: "He has been part of the team that has helped drive changes in the group. I'll be sad to see him go, but its a big career move for him."
Stephens, who first joined Ernest & Julio Gallo in 1994 as a sales representative, said he would take time to understand the challenges facing the Thresher business before deciding on a strategy.
"This is a fantastic opportunity to work with a pro-active team and a successful business. Multiple specialists are under extreme pressure as grocers move on to the high street, but I believe a healthy multiple specialist sector is critical for the UK market," he added.