North End will face the Blades on Friday, September 4 at a venue yet to be confirmed, with a 2pm kick-off.
A day later they will face the Toffees at Goodison Park, with a 2pm kick-off.
The club have also confirmed that their first round clash against Mansfield Town will take place on Saturday, August 29 at Deepdale.
After beating Salford City 3-1 in their opening pre-season friendly on Saturday, PNE face Tranmere Rovers away on Tuesday.
They are hopeful of arranging another friendly fixture before the Championship season kicks-off on September 12 at home to Swansea City