Electromagnetic topological chiral edge states mimicking the quantum Hall effect have attracted a great deal of attention due to their unique features of free backscattering and immunity against sharp bends and defects. However, the matching techniques between classical waveguides and the topological one-way waveguide deserve more attention for real-world applications. In this paper, a highly efficient conversion structure between a classical rectangular waveguide and a topological one-way waveguide is proposed and demonstrated at the microwave frequency, which efficiently converts classical guided waves to topological one-way edge states. A tapered transition is designed to match both the momentum and impedance of the classical guided waves and the topological one-way edge states. With the conversion structure, the waves generated by a point excitation source can be coupled to the topological one-way waveguide with very high coupling efficiency, which can ensure high transmission of the whole system (i.e., from the source and the receiver). Simulation and measurement results demonstrate the proposed method. This investigation is beneficial to the applications of topological one-way waveguides and opens up a new avenue for advanced topological and classical integrated functional devices and systems.