An intuitive on-site robot programming method for small-lot robotic welding is presented. In current robotic welding, a human operator has to input numerous parameters, including feedrate, swing width, and frequency, by using a teach pendant or a control panel before executing the task. This traditional approach is suitable for mass production, but requires tedious, time-consuming programming, which does not fit low-volume manufacturing, such as shipbuilding. In this paper, a method is developed for acquiring those parameters directly from an on-site human demonstration and seamlessly transitioning from manual operation to automatic control. With this method, a welding worker can directly execute a welding task, and the motion of a welding torch is observed, from which key parameters are identified and the machine performs the rest of the task autonomously. No tedious parameter input is required, but the worker can jump-start the task. The motion of a welding torch is represented as a combination of sinusoidal and linear functions. Discrete Fourier Transform (DFT) and Recursive Least Squares (RLS) estimates are used for identifying the parametric model in real time. Furthermore, an algorithm is developed for determining whether an appropriate estimation result has been obtained and when to switch from manual operation to autonomous control. The method is implemented on a virtual teleoperation system and seamless control transition is demonstrated.