The Seebeck effect describes the generation of an electric potential in a conducting solid exposed to a temperature gradient. In most cases, it is dominated by an energy-dependent electronic density of states at the Fermi level, in line with the prevalent efforts towards superior thermoelectrics through the engineering of electronic structure. Here we demonstrate an alternative source for the Seebeck effect based on charge-carrier relaxation: a charge mobility that changes rapidly with temperature can result in a sizeable addition to the Seebeck coefficient. This new Seebeck source is demonstrated explicitly for Ni-doped CoSb3, where a marked mobility change occurs due to the crossover between two different charge-relaxation regimes. Our findings unveil the origin of pronounced features in the Seebeck coefficient of many other elusive materials characterized by a significant mobility mismatch. When utilized appropriately, this effect can also provide a novel route to the design of improved thermoelectric materials.