Combination of H1 and ZEUS Deep Inelastic e+- p Scattering Cross Sections The previously published data by the H1 and the ZEUS collaborations of neutral and charged current inclusive cross-sections for $e^+p$ and $e^-p$ scattering at HERA are combined. The new model independent method of combining cross section measurements takes into account the systematic error correlations in a coherent approach leading to a significantly reduced overall cross section uncertainty by cross calibrating the various data sets. The analysis is restricted to data with momentum transfers $Q^2 \geq 1.5$\,GeV$^2$ and the running period HERA I, specifically between 1996-2000.