The discovery of high-temperature superconductivity in iron pnictides raised the possibility of an unconventional superconducting mechanism in multiband materials. The observation of Fermi-surface (FS)-dependent nodeless superconducting gaps suggested that inter-FS interactions may play a crucial role in superconducting pairing. In the optimally hole-doped Ba₀.₆K₀.₄Fe₂As₂, the pairing strength is enhanced simultaneously (2Δ/Tcalmost equal to7) on the nearly nested FS pockets, i.e., the inner hole-like (α) FS and the 2 hybridized electron-like FSs, whereas the pairing remains weak (2Δ/Tcalmost equal to3.6) in the poorly nested outer hole-like (β) FS. Here, we report that in the electron-doped BaFe₁.₈₅Co₀.₁₅As₂, the FS nesting condition switches from the α to the β FS due to the opposite size changes for hole- and electron-like FSs upon electron doping. The strong pairing strength (2Δ/Tcalmost equal to6) is also found to switch to the nested β FS, indicating an intimate connection between FS nesting and superconducting pairing, and strongly supporting the inter-FS pairing mechanism in the iron-based superconductors.