The 18-year-old midfielder, who became Spurs' youngest ever player when he made his debut two years ago, has been unable to hold down a place in the first-team squad.
Hull had been trying for some days to wrap up a deal for the England Under-19 star but were prevented from doing so due to what is thought to have been a Premier League probe into their finances.
It is unclear whether Bostock will be registered in time to make his debut in City's npower Championship opener against Swansea.
Last week saw the teenager vent his frustration at the lack of top-flight opportunities for young English players. He also admitted he was ready to go back out on loan after spending almost three months at Brentford last season.
Source: PA
Source: PA