The 18-year-old full-back, who began his career as a youth with the Tigers, played just a handful of times for the club last season.
He was an integral part of England's U20 squad at the Toulon Tournament where he played all five games as the Three Lions claimed victory, to retain the trophy they won last year.
A statement on the Potters' website read: "Tymon has signed a professional contract with the Potters having made his Premier League debut for the Tigers last season whilst still a scholar.
"The 18-year-old left-back started four top flight games for Hull and made one further league appearance as a substitute.
"Tymon also made two appearances in the FA Cup – he opened his first-team goal account in a 2-0 third round win over Swansea – and played a further five games in the EFL Cup."