The duo travelled with England as reserves on their winter tour of Sri Lanka and India, and were rewarded for impressive starts to their County Championship seasons with Gloucestershire and Sussex, respectively.
Head coach Chris Silverwood has also recalled Craig Overton, who last played in the 2019 Ashes series. Ben Stokes and Jofra Archer are ruled out through injury.
"James Bracey and Ollie Robinson deserve their call ups to the test squad. They have been consistent performers in the County Championship this season," Silverwood said.
"They are both resilient characters and have demonstrated... that they have the desire, temperament and the ability to continually improve to give themselves every chance of succeeding on the international stage."
England's Indian Premier League contingent, including Jos Buttler, Jonny Bairstow, Moeen Ali, Chris Woakes and Sam Curran, have been rested following the completion of their quarantine period last weekend after they returned from the subcontinent.
The series begins on June 2.
Squad: Joe Root (captain), James Anderson, James Bracey, Stuart Broad, Rory Burns, Zak Crawley, Ben Foakes, Dan Lawrence, Jack Leach, Craig Overton, Ollie Pope, Ollie Robinson, Dom Sibley, Olly Stone, Mark Wood.
