The invention provides an electrical heating solid heat storage boiler, and relates to the technical field of heating equipment. The electrical heating solid heat storage boiler comprises a boiler body, a supporting device, a heat storage device and a driver; the upper portion of the supporting device is arranged in the boiler body, and the heat storage device is connected with the supporting device and is arranged at one end of a water cooling wall of the boiler body; one end of the driver is connected with a first conveying pipe outside the boiler body, and the other end of the driver is connected with a second conveying pipe outside the boiler body; and a heater of the heat storage device is connected into a heat storage body. The problems that an existing boiler easily explodes, and pollution is large are solved. According to the electrical heating solid heat storage boiler, forced-convection heat transferring between high-temperature air heated through the heat storage body and the water cooling wall and radiation heat transferring between the heat storage body and the water cooling wall are used for heating low-temperature water in the water cooling wall, safety is good, and pollution is avoided. The invention further provides an electrical heating solid heat storage system, and multiple electrical heating solid heat storage boilers are connected through conveying pipes. The problem that the boiler burning heat efficiency is low is solved. The heat efficiency of the electrical heating solid heat storage boiler and the electrical heating solid heat storage system is high.