The Egypt winger will join Huddersfield on a three-year deal following the conclusion of the 2018 FIFA World Cup.
"He already has a lot of the qualities that we look for in our 'Terriers Identity'," head coach David Wagner told the club's official website.
"He’s skilful, direct and very quick-thinking. He still has a lot of space to improve too, which is very exciting."
Sobhi made 41 Premier League appearances since joining Stoke from Al Ahly in the summer of 2016.
The 21-year-old has scored two goals, including against Huddersfield, and provided one assist.
He is part of Egypt's squad at the 2018 FIFA World Cup in Russia.