Szoboszlai and Barnabas Varga were the team's four-goal joint leading scorers as they soared through qualifying to reach their third successive Euros, having missed out since 1972 previously.
Szoboszlai has made a fine start to his first season at English side Liverpool but has struggled for form since returning from injury earlier this year. Former Liverpool goalkeeper Peter Gulacsi is also named in the squad.
Rossi is taking a chance in his 26-man squad on veteran defenders Attila Fiola and Adam Lang as both have suffered injuries recently. However, the Italian manager has opted for experience as his team look to reach the last 16 for the first time since 2016.
Hungary squad
Goalkeepers: Denes Dibusz (Ferencvaros), Peter Gulacsi (RB Leipzig), Peter Szappanos (Paks)
Defenders: Botond Balogh (Parma), Endre Botka (Ferencvaros), Marton Dardai (Hertha BSC), Attila Fiola (Fehervar), Adam Lang (Omonia Nicosia), Willi Orban (RB Leipzig), Attila Szalai (Freiburg)
Midfielders: Bendeguz Bolla (Servette), Mihaly Kata (MTK), Milos Kerkez (Bournemouth), Laszlo Kleinheisler (Hajduk Split), Adam Nagy (Spezia Calcio), Zsolt Nagy (Puskas Akademia), Loic Nego (Le Havre), Andras Schafer (Union Berlin), Callum Styles (Sunderland)
Forwards: Martin Adam (Ulsan Hyundai), Kevin Csoboth (Ujpest), Daniel Gazdag (Philadelphia Union), Krisztofer Horvath (Kecskemet), Roland Sallai (Freiburg), Dominik Szoboszlai (Liverpool), Barnabas Varga (Ferencvaros).
