He will retire from the supermarket chain in January, after 15 years, to be replaced on a temporary basis by Caroline Massingham currently retail people director at George at Asda.
A spokeswoman from Asda said: "[Smith] has been planning for a short time to retire from Asda and in the New Year, he'll be leaving us to spend some time with his family and to explore speaking and consulting opportunities.
"An announcement on executive people director will be made in due course."