At 16 years and 295 days Bostock became Spursâ€™ youngest first-team player, beating Ally Dickâ€™s record by six days.
Redknapp said: "He is certainly a special young player. I saw John at Crystal Palace and he looked a terrific talent. Heâ€™s got a lovely left foot.
"How far he goes will be up to him and how hard he works. Iâ€™ve had loads of schoolboy players who look like world beaters who havenâ€™t made it."