The 21-year-old was released by Spurs last month after failing to make an impact at White Hart Lane.
He will link up with former Chelsea and Leeds striker Jimmy Floyd Hasselbaink, who was appointed as manager of the Second Division side in May.
Bostock tweeted: "Delighted to announce that I've signed for Royal Antwerp FC today. Can't wait to start the season and really looking forward to working under my new coach Jimmy Floyd Hasselbaink."
Bostock was regarded as one of the hot prospects in English football when he joined Tottenham from Crystal Palace in 2008 for an initial fee of £700,000.
However, he failed to establish himself at Spurs, making just three substitute appearances, and had loan spells at Brentford, Hull City, Sheffield Wednesday, Swindon Town and Toronto FC.
Andre Villas-Boas decided not to offer Bostock fresh terms when his five-year deal expired last month.
Royal Antwerp finished 10th in last season's Belgian Second Division, winning just 12 of their 34 games.