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In this paper we study the observational constraints that can be imposed on the coupling parameter, $\hat α$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| \hat α| \lesssim 10^{10} \,{\rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}\, {\rm s}$), or the immediate vicinity of stellar-mass black holes ($M\lesssim100\, M_{\odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $\hat α$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 \lesssim \hat α\lesssim 10^8 \, {\rm m}^2$.