Sobhi, 19, has grown into an influential figure at Al Ahly since making his debut two seasons ago, helping the club win two successive Egyptian Premier League titles.
The winger scored 17 goals in 71 appearances for Ahly and is one of his country’s most highly rated young players.
Stoke City chief exceutive Tony Scholes said: “We are absolutely delighted to have signed a player of Ramadan’s undoubted quality and potential.
“He’s a special young talent who is excited about the prospect of making an impact in the Premier League and we’re looking forward to giving him that platform.”
Sobhi’s dazzling dribbling and impeccable passing have previously seen him linked with some of Europe’s biggest clubs, including Atletico Madrid, Chelsea, Arsenal and Roma.
Affectionately nicknamed “Ramadona” by fans, Sobhi is set to join his new team-mates in Orlando, where they are currently in pre-season training ahead of the new Premier League season.