  We show that dynamical relaxation in the aftermath of a galactic merger and
the ensuing formation and decay of a binary massive black hole (MBH), are
dominated by massive perturbers (MPs) such as giant molecular clouds or
clusters. MPs accelerate relaxation by orders of magnitude relative to 2-body
stellar relaxation alone, and efficiently scatter stars into the binary MBH's
orbit. The 3-body star-binary MBH interactions shrink the binary MBH to the
point where energy losses from the emission of gravitational waves (GW) lead to
rapid coalescence. We model this process based on observed and simulated MP
distributions and take into account the decreased efficiency of the star-binary
MBH interaction due to acceleration in the galactic potential. We show that
mergers of gas-rich galactic nuclei lead to binary MBH coalescence well within
the Hubble time. Moreover, lower-mass binary MBHs (<10^8 Msun) require only a
few percent of the typical gas mass in a post-merger nucleus to coalesce in a
Hubble time. The fate of a binary MBH in a gas poor galactic merger is less
certain, although massive stellar structures (e.g. clusters, stellar rings)
could likewise lead to efficient coalescence. These coalescence events are
observable by their strong GW emission. MPs thus increase the cosmic rate of
such GW events, lead to a higher mass deficit in the merged galactic core and
suppress the formation of triple MBH systems and the resulting ejection of MBHs
into intergalactic space.
