The balloon-borne very long baseline interferometry (VLBI) experiment is a technical feasibility study for performing radio interferometry in the stratosphere. The flight model has been developed. A balloon-borne VLBI station will be launched to establish interferometric fringes with ground-based VLBI stations distributed over the Japanese islands at an observing frequency of approximately 20 GHz as the first step. This paper describes the system design and development of a series of observing instruments and bus systems. In addition to the advantages of avoiding the atmospheric effects of absorption and fluctuation in high frequency radio observation, the mobility of a station can improve the sampling coverage (`uv-coverage) by increasing the number of baselines by the number of ground-based counterparts for each observation day. This benefit cannot be obtained with conventional arrays that solely comprise ground-based stations. The balloon-borne VLBI can contribute to a future progress of research fields such as black holes by direct imaging.