  Gravitational-wave detectors are unveiling a population of binary black hole
(BBH) mergers out to redshifts $z \approx 1$, and are starting to constrain how
the BBH population evolves with redshift. We present predictions for the
redshift evolution of the BBH mass and spin distributions for systems
originating from dense star clusters. Utilizing a grid of 144 state-of-the-art
dynamical models for globular clusters, we demonstrate that BBH merger rates
peak at higher redshifts for larger black hole primary masses $M_1$.
Specifically, for $M_1\gtrsim40\,M_{\odot}$, the BBH merger rate reaches its
peak at redshift $z\approx2.1$, while for $M_1\lesssim20\,M_{\odot}$, the peak
occurs at $z\approx1.1$, assuming that the cluster formation rate peaks at
$z=2.2$. The average BBH primary mass also increases from $\sim 10\,M_{\odot}$
at $z=0$ to $\sim 30\,M_{\odot}$ at $z=10$. We show that $\sim 20\%$ BBHs
contain massive remnants from next-generation mergers, with this fraction
increasing (decreasing) for larger (smaller) primary masses. This difference is
not large enough to significantly alter the effective spins of the BBH
population originating from globular clusters, and we find that their effective
spin distribution does not evolve across cosmic time. These findings can be
used to distinguish BBHs from dense star clusters by future gravitational wave
observations.
