Smith will be replaced by James Simmons, who is currently customer director for Tesco at Unilever, after a handover period.
Smith has worked at Unilever for 28 years in senior roles including sales director and customer management director. He is also a former president of grocery charity Caravan.
Simmons joined Unilever in 1998 and has held a number of customer development and marketing roles, including UK trading director for Unilever Frozen Food & Ice Cream and customer director for Unilever Home & Personal Care.
"In James, I'm delighted to say that we have someone who has a great track record and has done a great job as home & personal care customer director and with Tesco across the whole Unilever portfolio," said Unilever executive vice president Dave Lewis. "He has a wealth of experience in customer development, has also been working closely with Tony for the past couple of years and now has a handover period in which to prepare for the challenges to come."
Simmons will be replaced by Steve Hermiston, who rejoins Unilever from Tate & Lyle, where he is retail sales and marketing director. He left Unilever during the Birds Eye disposal in 2007, having previously held a number of category management posts at Unilever's frozen food and ice cream business Birds Eye Wall's, including head of Asda's business unit.