The high rate of black hole (BH) mergers detected by LIGO/Virgo opened questions on their astrophysical origin. One possibility is the dynamical channel, in which binary formation and hardening is catalyzed by dynamical encounters in globular clusters (GCs). Previous studies have shown that the BH merger rate from the present day GC density in the Universe is lower than the observed rate. In this Letter, we study the BH merger rate by accounting for the first time for the evolution of GCs within their host galaxies. The mass in GCs was initially ∼8×higher, which decreased to its present value due to evaporation and tidal disruption. Many BH binaries that were ejected long before their merger originated in GCs that no longer exist. We find that the comoving merger rate in the dynamical channel from GCs varies between 18 to 35 Gpc^{-3} yr^{-1} between redshift z=0.5 to 2, and the total rate is 1, 5, 24 events per day within z=0.5, 1, and 2, respectively. The cosmic evolution and disruption of GCs systematically increases the present-day merger rate by a factor ∼2 relative to isolated clusters. Gravitational wave detector networks offer an unique observational probe of the initial number of GC populations and their subsequent evolution across cosmic time.