Mr Potts, who started his Tesco career at age 16 and rose to become retail director in the UK and chief executive of its Irish businesses, will take the helm on 16 March.
He takes over from Dalton Philips, who said in January he would leave the troubled supermarket after five years in charge.
The chain is battling falling sales.
It has been criticised for being slow in moving into the convenience store sector and setting up an online operation.
BBC News – Morrisons names David Potts as new chief executive http://t.co/EGwORSejx5
— Will Corry (@slievemore) February 25, 2015