The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported evidence for the presence of a common stochastic signal across their array of pulsars. The origin of this signal is still unclear. One of the possibilities is that it is due to a stochastic gravitational wave background (SGWB) in the $sim 1-10,{rm nHz}$ frequency region. Taking the NANOGrav observational result at face value, we show that this signal would be fully consistent with a SGWB produced by an unresolved population of in-spiralling massive black hole binaries (MBHBs) predicted by current theoretical models. Considering an astrophysically agnostic model we find that the MBHB merger rate is loosely constrained to the range $10^{-11} - 2$ $mathrm{Mpc}^{-3},mathrm{Gyr}^{-1}$. Including additional constraints from galaxy pairing fractions and MBH-bulge scaling relations, we find that the MBHB merger rate is $10^{-5} - 5times10^{-4}$ $mathrm{Mpc}^{-3},mathrm{Gyr}^{-1}$, the MBHB merger time-scale is $le 3,mathrm{Gyr}$ and the norm of the $M_mathrm{BH}-M_mathrm{bulge}$ relation $ge 1.2times 10^{8},M_odot$ (all intervals quoted at 90% confidence). Regardless of the astrophysical details of MBHB assembly, this result would imply that a sufficiently large population of massive black holes pair up, form binaries and merge within a Hubble time.
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