because electrons(electricity) travels from negative to positive, hence as the solution loses electrons to the anode and they pass through to the cathode, it is the negative electrode
Electrons flow along the external wire from anode to cathode. In a circuit (in Physics) electrons flow along a wire from negative to positive. Hence, in an electrochemical cell, anode = negative electrode, cathode = positive electrode.
Note - if you do Shipwrecks, Corrosion and Conservation, the situation is different for electrolytic cells.