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The 22-year-old was one of 10 players who left Oxford at the end of their contract in May after two years in OX4.
Knightbridge acted as a third-choice keeper during his time with the U's but never made a first team appearance.
The former England youth international has now signed for Premier League club Spurs after coming up through the academy of rivals West Ham United.
He will link up with the club's Under-21 setup.
The young shot-stopper had reportedly been on trial with National League outfit Southend United earlier this summer.
During his time at Oxford, Knightbridge was sent out on loan on two occasions with short-term spells at Braintree Town and AFC Totton, playing twice for the former and six times for the latter.
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