Recent development in fabrication technology of planar two-dimensional (2D) materials has brought up possibilities of numerous novel applications. Our recent analysis has revealed that by definition of p-n junctions through appropriate patterned doping of 2D semiconductors, ideal exponential I-V characteristics may be expected. However, the theory of 2D junctions turns out to be very much different to that of the standard bulk junctions. Based on this theory of 2D diodes, here we construct for the first time, a model to describe the 2D Bipolar Junction Transistors (2D-BJTs). We derive the small-signal equivalent model, and estimate the performance of a 2D-BJT device based on Graphone as the example material. A current gain of about 138 and maximum threshold frequency of 77GHz, together with a power-delay product of only 4fJ per 1um lateral width is expected at an operating voltage of 5V. Also, we derive necessary formulae and a new approximate solution for continuity equation in the 2D configuration, which have been verified against numerical solutions.