Ben Stokes and fast bowler Gus Atkinson were dropped after breaking a midnight curfew in an incident at a London nightclub following England's first Test win at Lord's.
Gattuso returns to club coaching in Serie A, where he was one of the faces of a star-studded AC Milan team which over his 13 years at the San Siro won two Serie A titles and the Champions League in 2003 and 2007.