Light-emitting diodes (LEDs) are becoming increasingly high-power and compact, which makes rotary fans incompetent in some cooling situations. The ionic wind technique can compensate for the shortcomings of rotating fans, owing to its benefits of no moving parts and compact structure. Integrating the ionic wind generator with heat dissipation fins can effectively reduce the size of LED devices, but research in this area is still insufficient. In this study, an integrated ionic wind heat sink is designed for cooling LEDs. The multi-physical characteristics of discharge, flow, and heat transfer are numerically studied. The geometric parameters’ impact degree and mechanism on the multi-physical characteristics are analyzed. The performance optimization of the integrated heat sink is realized and verified. The fin length, flow channel center angle, and relative position of the fin have a large influence on the average velocity of ionic wind. The relative position of the wire electrode determines the electric field strength distribution, and it has the greatest influence on the ionic wind performance. The emitting electrode being placed at the inlet edge of the collecting electrode produces a high ionic wind flow rate. The integrated ionic wind heat sink designed in this study exhibits an outstanding cooling performance and temperature uniformity. This device can cool down the surface of a heat source with a power of 200 W to below 91 °C and make the average heat transfer coefficient reach 18.6 W/(m2·K). This study proposes a valuable method to optimize the integrated ionic wind heat sink for cooling high-power electronic devices.