Fleet said on their website that Spurs had sealed the deal for an undisclosed fee and beat off competition from the likes of Charlton Athletic, Crystal Palace, Ipswich Town, Reading and West Ham United.
"This is a fantastic opportunity for Shilow and we are proud of the fact that our youth academy is producing quality young players just one year after we set it up," Fleet vice-chairman Peter Varney told the club website.
"I would like to thank Spurs for the professional manner in which they have handled the transfer negotiations. I must also recognise the work done with Shilow by Daryl McMahon and his staff in our youth academy."
Tracey, a midfielder, was first invited for a trial with Spurs in October and then travelled with the North London side's Under-18s to play at the IMG Cup in Florida last month.