Onshore penetration of oceanic water across the Antarctic continental slope (ACS) plays a major role in global sea level rise by delivering heat to the Antarctic marginal seas, thus contributing to the basal melting of ice shelves. Here, the time‐mean (Φmean) and eddy (Φeddy) components of the heat transport (Φ) across the 1000 m isobath along the entire ACS are investigated using a 0.1° global coupled ocean/sea ice simulation based on the Los Alamos Parallel Ocean Program (POP) and sea ice (CICE) models. Comparison with in situ hydrography shows that the model successfully represents the basic water mass structure, with a warm bias in the Circumpolar Deep Water layer. Segments of on‐shelf Φ, with lengths of O(100‐1000 km), are found along the ACS. The circumpolar integral of the annually‐averaged Φ is O(20 TW), with Φeddy always on‐shelf, while Φmean fluctuates between on‐shelf and off‐shelf. Stirring along isoneutral surfaces is often the dominant process by which eddies transport heat across the ACS, but advection of heat by both mean flow‐topography interactions and eddies can also be significant depending on the along‐ and across‐slope location. The seasonal and interannual variability of the circumpolarly‐integrated Φmean is controlled by convergence of Ekman transport within the ACS. Prominent warming features at the bottom of the continental shelf (consistent with observed temperature trends) are found both during high‐SAM and high‐Niño 3.4 periods, suggesting that climate modes can modulate the heat transfer from the Southern Ocean to the ACS across the entire Antarctic margin.