Cescau left Unilever just two weeks ago and is the third heavyweight non-exec to be secured by Tesco in the past two months.
Last month, Tesco said former Cadbury Schweppes chief financial officer Ken Hanna and former director general of the Netherlands Ministry of Transport Jacqueline Tammenoms Bakker would be joining the board this year.
They filled gaps left by Mervyn Davies, chairman of Standard Chartered, and Carolyn McCall, chief executive of Guardian Media Group, who left Tesco non-exec roles last year because of conflicts of interest.
Reid, 61, has been non-exec chairman at Tesco since 2004 and has served on the board since 1985.
Although Tesco has given no indication as to when he could stand down, none of its non-execs are tied into incentive plans like its executive directors.
But Reid was in no hurry to leave Tesco, said Dave McCarthy, an analyst at Hobart Capital. “I don’t think there is any pressure on David to go, I get no impression that is the case.”
Cescau was CEO of Unilever from 2005 until his retirement on 1 January. He joins Tesco on 1 February. His experience and knowledge of consumer goods and international perspective, which includes extensive experience of the Indian market, would be valuable to the board of directors, Tesco said.