Fast oxygen transport materials are necessary for a range of technologies, including efficient and cost-effective solid oxide fuel cells, gas separation membranes, oxygen sensors, chemical looping devices, and memristors. Strain is often proposed as a method to enhance the performance of oxygen transport materials, but the magnitude of its effect and its underlying mechanisms are not well-understood, particularly in the widely-used perovskite-structured oxygen conductors. This work reports on an ab initio prediction of strain effects on migration energetics for nine perovskite systems of the form LaBO₃, where B = [Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Ga]. Biaxial strain, as might be easily produced in epitaxial systems, is predicted to lead to approximately linear changes in migration energy. We find that tensile biaxial strain reduces the oxygen vacancy migration barrier across the systems studied by an average of 66 meV per percent strain for a single selected hop, with a low of 36 and a high of 89 meV decrease in migration barrier per percent strain across all systems. The estimated range for the change in migration barrier within each system is ±25 meV per percent strain when considering all hops. These results suggest that strain can significantly impact transport in these materials, e.g., a 2% tensile strain can increase the diffusion coefficient by about three orders of magnitude at 300 K (one order of magnitude at 500 °C or 773 K) for one of the most strain-responsive materials calculated here (LaCrO₃). We show that a simple elasticity model, which assumes only dilative or compressive strain in a cubic environment and a fixed migration volume, can qualitatively but not quantitatively model the strain dependence of the migration energy, suggesting that factors not captured by continuum elasticity play a significant role in the strain response.