ABSTRACT We present cross-correlation studies of γ-ray (0.1–300 GeV), X-ray (0.2–10 keV), and optical (R band) variability of a sample of 26 blazars during 2008–2016. The light curves are from Fermi-LAT, Swift-XRT, and the Yale-SMARTS blazar monitoring program. We stack the discrete cross-correlation functions of the blazars such that the features that are consistently present in a large fraction of the sample become more prominent in the final result. We repeat the same analysis for two subgroups, namely, low synchrotron peaked (LSP) and high synchrotron peaked (HSP) blazars. We find that, on average, the variability at multiple bands is correlated, with a time lag consistent with zero in both subgroups. We describe this correlation with a leptonic model of non-thermal emission from blazar jets. By comparing the model results with those from the actual data, we find that the inter-band cross-correlations are consistent with an emission region of size 0.1 pc within the broad-line region for LSP blazars. We rule out large changes of magnetic field (>0.5 Gauss) across the emission region or small values of magnetic field (e.g., 0.2 Gauss) for this population. We also find that the observed variability of the HSP blazars can be explained if the emission region is much larger than the distance to the broad-line region from the central black hole.