A confident Fury had the better of the early rounds as he danced around his opponent's attempted jabs before he landed a sharp uppercut at the end of round two, while a neat combo gave him the third round as well.
The 26-year-old stepped up a level in the fifth round as he caught Hammer with a big shot that sent him crashing to the floor.
Although he beat the count, Hammer clearly looked dazed and only the referee's bell saved him from a fifth-round defeat as Fury continued to pile on the pressure.
Hammer continued to throw wayward shots in the sixth round and Fury coped with them comfortably before he landed some massive body shots in round seven.
After more uppercuts from Fury, Hammer threw in the towel at the end of the eighth round and the crowd booed at the disappointing ending.
In the celebrations Fury shouted "Klitschko next", in reference to a potential summer fight with Wladimir Klitschko.