A flush water tank apparatus for supplying flush water to a flush toilet, the flush water tank apparatus comprising: a storage tank storing flush water to be supplied to the flush toilet, with a drain port for discharging the stored flush water to the flush toilet formed therein; a discharge valve configured to open and close the drain port and performing supply and stop of the flush water to the flush toilet; a discharge valve hydraulic drive unit driving the discharge valve using water supply pressure of supplied tap water; a clutch mechanism coupling the discharge valve and the discharge valve hydraulic drive unit to pull up the discharge valve by driving force of the discharge valve hydraulic drive unit, and being disconnected at a predetermined timing to cause the discharge valve to descend; a flush water amount selection device (6, 40) capable of selecting between a first amount of flush water for washing the flush toilet and a second amount of flush water smaller than the first amount of flush water; a first float device comprising a first float moved according to a water level in the storage tank and a first engaging member capable of moving to an engaging position of engaging with the discharge valve to hold the discharge valve and a non-engaging position of not engaging with the discharge valve in conjunction with movement of the first float; a second float device comprising a second float moved according to the water level in the storage tank and a second engaging member capable of moving to an engaging position of engaging with the discharge valve and a non-discharging position of not engaging with the discharge valve in conjunction with movement of the second float and causing the second engaging member to move to the non-engaging position at a height different from a height at which the first float causes the first engaging member to move to the non-engaging position; and a float driving mechanism driving the first float to cause the first engaging member to move to the non-engaging position when the second amount of flush water is selected by the flush water amount selection device; wherein by the first engaging member of the first float device being moved to the non-engaging position, the discharge valve engages with the second engaging member of the second float device. a storage tank storing flush water to be supplied to the flush toilet, with a drain port for discharging the stored flush water to the flush toilet formed therein; a discharge valve configured to open and close the drain port and performing supply and stop of the flush water to the flush toilet; a discharge valve hydraulic drive unit driving the discharge valve using water supply pressure of supplied tap water; a clutch mechanism coupling the discharge valve and the discharge valve hydraulic drive unit to pull up the discharge valve by driving force of the discharge valve hydraulic drive unit, and being disconnected at a predetermined timing to cause the discharge valve to descend; a flush water amount selection device (6, 40) capable of selecting between a first amount of flush water for washing the flush toilet and a second amount of flush water smaller than the first amount of flush water; a first float device comprising a first float moved according to a water level in the storage tank and a first engaging member capable of moving to an engaging position of engaging with the discharge valve to hold the discharge valve and a non-engaging position of not engaging with the discharge valve in conjunction with movement of the first float; a second float device comprising a second float moved according to the water level in the storage tank and a second engaging member capable of moving to an engaging position of engaging with the discharge valve and a non-discharging position of not engaging with the discharge valve in conjunction with movement of the second float and causing the second engaging member to move to the non-engaging position at a height different from a height at which the first float causes the first engaging member to move to the non-engaging position; and a float driving mechanism driving the first float to cause the first engaging member to move to the non-engaging position when the second amount of flush water is selected by the flush water amount selection device; wherein by the first engaging member of the first float device being moved to the non-engaging position, the discharge valve engages with the second engaging member of the second float device.