Bostock, who joined Spurs from Crystal Palace, became the youngest player to represent Spurs when at the age of 16 he came off the bench in a UEFA Cup tie against Dinamo Zagreb.
Bees boss Andy Scott is pleased to land the 17-year-old and he is expected to go straight into the squad for this weekend's London derby with Millwall.
"I'm delighted to have signed John as he has been highly rated for several years as was proved by him signing for Tottenham at the age of 16," Scott told the club's official website.
"Spurs are looking for him to progress and force his way into the first-team reckoning and they feel that here at Brentford he will have the opportunity to show his worth. From our perspective it will give some added quality and dimension to our play."
Bostock is looking forward to his spell at the League One outfit.
"I'm really pleased to be joining Brentford," he said. "I know a bit about the club and football in this league as some of my team-mates at Spurs are on loan at Yeovil and Leyton Orient.
"It's a good league and I'm looking forward to playing in it for Brentford"
Another player to depart White Hart Lane is midfielder Sam Cox who has joined Histon FC on a one-month loan deal.