The anomalous Hall (AH) effect measurement has emerged as a powerful tool to gain deep insights into magnetic materials, such as ferromagnetic metals, magnetic semiconductors, and magnetic topological insulators (TIs). In Mn-doped Bi2Se3, however, the AH effect has never been reported despite a lot of previous studies. Here we report the observation of AH effect in (Bi,Mn)2Se3 thin films and show that the sign of AH resistances changes from positive to negative as the Mn concentration is increased. The positive and negative AH resistances are found to coexist in a crossover regime. Such a two-component AH effect and the sign reversal can also be obtained by electrical gating of lightly doped samples. Our results provide an important basis for understanding the puzzling interplay between the surface states, the bulk states, and various magnetic doping effects, as well as competing magnetic orders in magnetically doped TIs.