  Since the recent derivation of a well-defined $D\rightarrow 4$ limit for
regularized 4D Einstein Gauss-Bonnet (4DEGB) gravity, there has been
considerable interest in testing it as an alternative to Einstein's general
theory of relativity. In this paper we construct slowly rotating black hole
solutions for 4DEGB gravity in asymptotically flat, de Sitter, and anti-de
Sitter spacetimes. At leading order in the rotation parameter, exact solutions
of the metric functions are derived and studied for all three of these cases.
We compare how physical properties (innermost stable circular orbits, photon
rings, black hole shadow, etc.) of the solutions are modified by varying
coupling strengths of the 4DEGB theory relative to standard Einstein gravity
results. We find that a vanishing or negative cosmological constant in 4DEGB
gravity enforces a minimum mass on the black hole solutions, whereas a positive
cosmological constant enforces both a minimum \textit{and} maximum mass with a
horizon root structure directly analogous to the Reissner-Nordstr\"om de Sitter
spacetime. Besides this, many of the physical properties are qualitatively
similar to general relativity, with the greatest deviations typically being
found in the low (near-minimal) mass regime.
