In this paper, two techniques based on Q-learning and action dependent heuristic dynamic programming (ADHDP) are demonstrated for the demand-side management of domestic electric water heaters (DEWHs). The problem is modeled as a dynamic programming problem, with the state space defined by the temperature of output water, the instantaneous hot water consumption rate, and the estimated grid load. According to simulation, Q-learning and ADHDP reduce the cost of energy consumed by DEWHs by approximately 26% and 21%, respectively. The simulation results also indicate that these techniques will minimize the energy consumed during load peak periods. As a result, the customers saved about $466 and $367 annually by using Q-learning and ADHDP techniques to control their DEWHs (100 gallons tank size) operation, which is better than the cost reduction that resulted from using the state-of-the-art ($246) control technique under the same simulation parameters. To the best of the authors' knowledge, this is the first work that uses the approximate dynamic programming techniques to solve the DEWH's load management problem.