The detection of a dipole anisotropy in the sky distribution of sources in large-scale radio surveys can be used to constrain the magnitude and direction of our local motion with respect to an isotropically distributed extragalactic radio source population. Such a population is predicted to be present at cosmological redshifts in an isotropically expanding universe. The extragalactic radio source population is observed to have a median redshift of z ~ 1, a much later epoch than the cosmic microwave background (z ~ 1100). I consider the detectability of a velocity dipole anisotropy in radio surveys having a finite number of source counts. The statistical significance of a velocity dipole detection from radio source counts is also discussed in detail. I find that existing large-scale radio survey catalogs do not have a sufficient number of sources to detect the expected velocity dipole with statistical significance, even if survey masking and flux calibration complications can be completely eliminated (i.e., if both the surveys and observing instruments are perfect). However, a dipole anisotropy should be easily detectable in future radio surveys planned with next-generation radio facilities, such as the Low Frequency Array and the Square Kilometer Array; tight constraints on the dipole magnitude and direction should be possible if flux calibration problems can be sufficiently minimized or corrected and contamination from local sources can be eliminated.