Jofra Archer has also been able to retain his spot in the 12-man squad announced on Friday, making his chances brighter for a Test debut next week.
Moeen's lackluster performance in England's crushing 251-run defeat at Edgbaston forced the selectors to drop him for the second game.
The 32-year-old could manage just 4 runs across the two innings and returned match figures of 3-172, epitomizing his abysmal run in international cricket over the past few months.
The Somerset left-arm spinner Leach has so far played five Tests for England and was adjudged man of the match for his career-best 92 against Ireland last month when he came in to bat as a nightwatchman.
Leach was also impressive during England's tour to Sri Lanka in November where he achieved the most number wickets for his side - equal with Moeen (18).
Although Archer was named in England's 14-man squad for the first Test, he was left out of the side to recover from his side strain.
The 24-year-old speedster exhibited a grand all-round show in a second-team match for county side Sussex as he racked up a century and took six wickets in a hostile spell of fast bowling.
England's injury list has grown over the summer with Olly Stone and Mark Wood also being ruled out of the cricket action owing to their fitness concerns.
The other pace bowling option for England in the squad is left-armer Sam Curran who has played 10 Tests for his country.
Despite middle-order batting frailties showing up during the first Ashes Test, England have persisted with the same combination as Joe Denly, Jonny Bairstow and Jos Buttler have managed to hold their place in the team.
Joe Root (c), Rory Burns, Jason Roy, Joe Denly, Jos Buttler, Jonny Bairstow (wk), Ben Stokes, Chris Woakes, Jofra Archer, Stuart Broad, Jack Leach, Sam Curran