The upper critical field Hc2 in superconducting BaFe2-xNixAs2 single crystals has been determined by magnetotransport measurements down to 0.6 K over the whole superconducting dome with 0.065≤x≤0.22 for both the interplane (H¥c,Hc2c) and in-plane (H¥ab,Hc2ab) field directions in static magnetic fields up to 16 T and pulsed magnetic fields up to 60 T. The temperature dependence of Hc2ab follows the Werthamer-Helfand-Hohenberg model incorporating orbital and spin paramagnetic effects, while Hc2c(T) can only be described by the effective two-band model with unbalanced diffusivity. The anisotropy of the upper critical fields, γ(T)=Hc2ab/Hc2c, monotonically increases with increasing temperature for all dopings, and its zero-temperature limit γ(0) has an asymmetric doping dependence with a significant enhancement in the overdoped regime, where the optimally doped compound has the most isotropic superconductivity. Our results suggest that the anisotropy in the superconductivity of iron pnictides is determined by the topology of the Fermi surfaces together with the doping-induced impurity scattering.