Fast bowlers Mark Wood and Jofra Archer were not considered for selection because both players have suffered side strains.
Roy, 28, has not played a first-class match since November and batted only three times in Surrey's winning County Championship campaign last summer, scoring one hundred and a fifty.
Wood is expected to be out of action for four to six weeks following the injury he sustained in Sunday's final, leaving him certain to miss the start of the five-Test Ashes.
He will have a short break in Barbados before returning to the United Kingdom later this month.
The trio are also included in a 16-man group for a pre-Ashes camp. He has now been rewarded with a spot in the Test squad for the one-off match against Ireland, which is scheduled to get underway on July 24 at the Lord's in London.
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After Eoin Morgan captained England's World Cup team, it is Joe Root who resumed his role as Test skipper against Ireland.
James Anderson is included in both squads but may not play against Ireland as he continues his rehabilitation from a calf injury although Smith admitted it's not clear when the veteran seamer will be available.
Gregory, the 27-year-old Somerset bowling all-rounder, is promoted after impressing at Taunton and in the England Lions programme and has taken 44 wickets this season at an average of just 13.88.
Sam Curran hit his second half-century of the match as England Lions secured a draw in their four-day encounter with Australia A at Canterbury.
Stone, who was an unused squad member on last year's Test series in Sri Lanka, was forced to sit out the subsequent tour of the Caribbean earlier this year, after picking up a stress fracture of the back.
England squad in full for pre-Ashes camp: Moeen Ali, James Anderson, Jonny Bairstow, Stuart Broad, Rory Burns, Jos Buttler, Sam Curran, Joe Denly, Lewis Gregory, Jack Leach, Joe Root, Jason Roy, Ben Stokes, Olly Stone, Chris Woakes, Mark Wood.