Stoke expressed an interest in the 19-year-old back in May, but their first offer was turned down by Al Ahly.
However, Mark Hughes returned with another bid for the highly-rated teenager and had a fee of £2.5m with a few add-ons accepted by his club.
Sobhi is unlikely to get a work permit as he has played only six matches for the Egyptian national team and Stoke are set to loan him out.
The wide-man is seen as a great prospect for the future and scored five goals last season as Al Ahly captured the league title.
Al Ahly boss Martin Jol told ONtv that the youngster went about his business in the right way as he wanted to play against arch-rivals Zamalek despite being on the verge of moving.
"If he goes, he did it in a good way, and that’s better than doing it in a bad way," Jol said.
"I am very proud of Ramadan Sobhi, he insisted on playing. We’re preparing a farewell party for him soon."