We derive expressions for strangeness-changing scalar form factors, which incorporate known theoretical constraints both at low and high energies. Their leading behaviour in the limit of a large number of colours is calculated from the resonance chiral Lagrangian, and a set of short-distance constraints on the scalar resonance couplings is obtained, imposing the form factors to vanish at infinite momentum transfer. The important effects of meson rescattering are taken into account by exploiting unitarity and analyticity. Making use of previous results on S-wave Kpi scattering [1], and a coupled-channel dispersion-relation analysis, the Kpi, Keta and Keta' scalar form factors are calculated up to 2 GeV These scalar form factors are a key ingredient in the determination of the corresponding scalar spectral function which is important in the extraction of the mass of the strange quark from QCD sum rules as well as hadronic tau decays.