Oceanic Rossby waves and eddies flux energy and fluid westward, the latter through the Stokes drift or bolus transport. While the wave energy is largely dissipated at the western boundary, mass conservation requires that the fluid be returned offshore through Rossby rip currents. The form and magnitude of these rip currents are investigated through linear Rossby wave theory, a nonlinear numerical model, and analysis of sea surface height satellite observations. The net eastward volume transport by Rossby rip currents over the global ocean is estimated to be of order 10 Sv (1 Sv ≡106 m3 s−1). In an eddying ocean, both the westward Stokes drift and eastward rip currents can assume the form of banded quasi‐zonal jets.