Modular tankless water heater apparatus designed for use in a system including a water supply conduit and a hot water conduit. The apparatus includes a heating tube assembly with a plurality of tubes positioned in parallel juxtaposition and connected adjacent the ends into a series connected configuration to form a continuous fluid passage. A heating element is enclosed in each tube and extends between the ends with each heating element including an electrical connector and an electrical control. A programmable electrical power controller is connected to the electrical controls of the heating elements and to flow sensor and heat sensor apparatus positioned in the continuous fluid passage. The controller is programmed to activate the electrical controls one at a time in response to a demand signal from the flow sensor and heat sensor apparatus.