Based on the chaos polarization system of external optical feedback injection vertical cavity surface emitting laser (VCSEL) and the theory of linear electro-optic modulation, a reconfigurable opto-electronic chaotic logic gate is proposed and its physical model is given in this paper. First, the parameter space, such as applied electric field and optical feedback intensity, is determined when VCSEL output light is chaotic state. Then, the external electric field is modulated as the gating factor, the optical feedback intensity is modulated as the logic input, and the logic output is demodulated by threshold mechanism. When the logic input and gating factor satisfy different logic operation relations, the system can switch different chaotic logic gates flexibly, such as AND, NAND, OR, NOR, XOR, and XNOR.