Lower the float into the water to make the valve shut off sooner...
Alternatively if the valve has a nylon adjuster screw then turn it inwards towards the valve and then tighten the locking nut - this is the same as lowering the float.
If it still dribbles then the rubber seal in the valve may well have perished.
The syphon is more than probably perfectly OK because the flush mechanism works - you have an overflow into the pan. Modern systems do this but the older ones overflowed outside. The inlet valve mechanism needs adjustment or repair.
Peccavi
September 2009