He will leave the FTSE 100-listed firm next April.
The board is to get a new look with Ken Murphy joining the company on October 1 to replace Dave Lewis as chief executive.
Lewis announced his departure last October for personal reasons after six years in the role, which came as a surprise.
“It is all consuming. The business never sleeps. It is 365 days, 24/7. I want to take some proper time out with my family and recharge my batteries. You pass this way only once,” he had told The Guardian.
The supermarket chain said Stewart played an “instrumental” role in the turnaround of the company, leading the corporate restructuring and rebuilding the balance sheet.
Tesco, which has seen higher demand during lockdown period, may continue to experience good sales throughout 2020 as out-of-home eating is unlikely to return to previous levels for a while yet.
"The achievements from those days of financial year 2015 are notable and no more so than the radically improved financial constitution of the Group, for which we give him considerable credit," analysts at Shore Capital commented.
"Tesco post the pending South-East Asia disposal will have notably lower net debt, an improved freehold/leasehold mix, a wholly manageable pension position, investment grade debt and an operating company that has the considerable potential to sustain progressively growing dividend flows and to notably buy-back shares."
Shares dipped 1% to 230.3p on Tuesday morning.
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