Transient light-induced absorption in nominally undoped and Fe-doped ${\text{KNbO}}_{3}$ crystals is observed in the visible and infrared spectral ranges after single pulse illumination with $\ensuremath{\lambda}=532\text{ }\text{nm}$. For nominally undoped ${\text{KNbO}}_{3}$ the decay of the light-induced absorption in a single step can be explained by incoherent hopping transport of optically generated small bound ${\text{O}}^{\ensuremath{-}}$ hole and small free ${\text{Nb}}^{4+}$ electron polarons and their mutual recombination. Iron doping causes an additional slow decay component and, remarkably, accelerates the initial decay process. A consistent model for the formation, hopping, and recombination paths of hole and electron polarons is deduced from the experimental data set for both nominally undoped and Fe-doped ${\text{KNbO}}_{3}$. The decrease in the polaron hopping-transport length in Fe-doped samples is attributed to the increased number densities of optically generated hole polarons by additional one-quantum excitations.