The FIRAS instrument on the COBE has determined the dipole spectrum of the cosmic microwave background radiation (CMBR) from 2 to 20 cm^-1^, For each frequency the signal is decomposed by fitting to a monopole, a dipole, and a Galactic template for ~60% of the sky. The overall dipole spectrum fits the derivative of a Planck function with an amplitude of 3.343 +/- 0.016 mK (95% confidence level), a temperature of 2.714 +/- 0.022 K (95% confidence level), and an rms deviation of 6 x 10^-9^ ergs cm^-2^ s^-1^ sr^-1^ cm limited by detector and cosmic-ray noise. The monopole temperature is consistent with that determined by direct measurement in the accompanying article by Mather et al.