The 22Ne(α, n)25Mg reaction is an important source of neutrons for the s-process. In massive stars responsible for the weak component of the s-process, 22Ne(α, n)25Mg is the dominant source of neutrons, both during core helium burning and in carbon-shell burning. For the main s-process component produced in asymptotic giant branch (AGB) stars, the 13C(α, n)16O reaction is the dominant source of neutrons operating during the interpulse period, with the 22Ne + α source affecting mainly the s-process branchings during a thermal pulse. Rate uncertainties in the competing 22Ne(α, n)25Mg and 22Ne(α, γ)26Mg reactions result in large variations of s-process nucleosynthesis. Here, we present up-to-date and statistically rigorous 22Ne + α reaction rates using recent experimental results and Monte Carlo sampling. Our new rates are used in postprocessing nucleosynthesis calculations both for massive stars and AGB stars. We demonstrate that the nucleosynthesis uncertainties arising from the new rates are dramatically reduced in comparison to previously published results, but several ambiguities in the present data must still be addressed. Recommendations for further study to resolve these issues are provided.