Twenty sites in the area have already been secured and additional locations are being researched.
The area has been chosen for the launch because of its high population growth and the strong potential of its expanding market.
Tesco will also be opening stores in Las Vegas, Los Angeles and San Diego.
Tim Mason, who now has the title of Fresh & Easy Neighborhood Market CEO, said that each of the stores would be roughly 10,000 sq ft in size in a bid to give US customers a faster and easier shopping experience than they currently got from a typical American supermarket.
Mason told an audience at the Greater Phoenix Economic Council that the retailer was determined to be a good neighbour and and an environmentally friendly business.