At 16 years and 295 days Bostock became Spurs’ youngest first-team player, beating Ally Dick’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. He’s got a lovely left foot.
"How far he goes will be up to him and how hard he works. I’ve had loads of schoolboy players who look like world beaters who haven’t made it."