We present the 3-8 keV and 8-24 keV number counts of active galactic nuclei (AGN) identified in the NuSTAR extragalactic surveys. NuSTAR has now resolved 33-39% of the X-ray background in the 8-24 keV band, directly identifying AGN with obscuring columns up to approximately 1e25 /cm2. In the softer 3-8 keV band the number counts are in general agreement with those measured by XMM-Newton and Chandra over the flux range 5e-15 < S(3 - 8 keV)/(erg/cm2/s) < 1e-12 probed by NuSTAR. In the hard 8-24 keV band NuSTAR probes fluxes over the range 2e-14 < S(8-24 keV)/(erg/cm2/s) < 1e-12, a factor of approximately 100 fainter than previous measurements. The 8-24 keV number counts match predictions from AGN population synthesis models, directly confirming the existence of a population of obscured and/or hard X-ray sources inferred from the shape of the integrated cosmic X-ray background. The measured NuSTAR counts lie significantly above simple extrapolation with a Euclidian slope to low flux of the Swift/BAT 15-55 keV number counts measured at higher fluxes S(15-55 keV) > 1e-11 erg/cm2/s, reflecting the evolution of the AGN population between the Swift/BAT local (z<0.1) sample and NuSTARs z~1 sample. CXB synthesis models, which account for AGN evolution, lie above the Swift/BAT measurements, suggesting that they do not fully capture the evolution of obscured AGN at low redshifts.