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.
Current Morrisons chairman Andrew Higginson was previously the finance director at Tesco and worked with Mr Potts there for 15 years. He said was "delighted" by the appointment.
"David is the best retailer I have worked with in 25 years in the industry. Having worked alongside him for 15 years, I know he will bring to Morrisons a focus on the customer, a track record of delivery, flair, talent, and immense energy to his new role," he added.
Morrisons is being squeezed between the higher end of the market and the discount supermarkets chains.
The Bradford-based company reported a 3.1% drop in like-for-like sales in the six weeks to 4 January, and said it would close 10 loss-making stores this year.
Mr Potts will be tasked with returning the company to growth.
He said it "was an honour to have been selected".
Morrisons has named former Tesco director David Potts as its new chief executive.