The $ab$-plane resistivity and Hall effect are studied in Fe$_{1-y}$M$_y$Te$_{0.65}$Se$_{0.35}$ single crystals doped with two transition metal elements, M = Co or Ni, over a wide doping range, $0 \leq y \leq 0.2$. The superconducting transition temperature, $T_{c}$, reaches zero for Co at $y \simeq 0.14$ and for Ni at $y \simeq 0.032$, while the resistivity at the $T_{c}$ onset increases weakly with Co doping, and strongly with Ni doping. The Hall coefficient $R_H$, positive for $y$ = 0, remains so at high temperatures for all $y$, while it changes sign to negative at low $T$ for $y > 0.135$ (Co) and $y > 0.06$ (Ni). The analysis based on a two band model suggests that at high $T$ residual hole pockets survive the doping, but holes get localized upon the lowering of $T$, so that the effect of the electron doping on the transport becomes evident. The suppression of the $T_c$ by Co impurity is related to electron doping, while in case of the Ni impurity strong electron localization most likely contributes to fast decrease of the $T_c$.