The controllable and wide-range modulation of the carrier type and mobility in atomically thin two-dimensional (2D) materials is one of the most critical issues to be addressed before 2D materials can be practically used for future electronic and optoelectronic devices. In this work, we propose using a novel surface charge transfer mechanism to accomplish the controllable and wide-range modulation of the carrier type and mobility in 2D materials. Our methodology uses a solution of triphenylboron (TPB) to physically coat 2D materials; the TPB molecule contains positive and negative charge centers that are spatially separable when induced by an electrical field. Consequently, the TPB can transfer either positive or negative charges to 2D materials depending on the direction of the applied electrical field and thus enhance the ambipolar behavior of the 2D-material FET. This method is so versatile that seven types of 2D materials including graphene, black phosphorus and five transition metal dichalcogenides (TMDCs) can be modulated to strong ambipolar behavior with significantly increased conduction. In addition, selectively suppressing or enhancing the negative charge center enables solely p-type and n-type doping. We also accomplish the precise tuning of carrier mobility in TMDCs from ambipolar to p-type by coating a mixture of TPB/BCF in certain concentration ratios.