The Antarctic Slope Current (ASC) and Antarctic Coastal Current advect heat, freshwater, nutrients, and biological organisms westward around the Antarctic margin, providing a connective link between different sectors of the continental shelf. Yet the strength and pathways of connectivity around the continent, and the timescales of advection, remain poorly understood. We use daily velocity fields from a global high‐resolution ocean‐sea ice model, combined with Lagrangian particle tracking, to shed light on these timescales and improve our understanding of circumpolar connectivity around Antarctica. Virtual particles were released along vertical transects over the continental shelf every 5 days for a year and were tracked forward in time for 21 years. Analysis of the resulting particle trajectories highlights that the West Antarctic sector has widespread connectivity with all regions of the Antarctic shelf. Advection around the continent is typically rapid with peak transit times of 1–5 years for particles to travel 90° of longitude downstream. The ASC plays a key role in driving connectivity in East Antarctica and the Weddell Sea, while the Coastal Current controls connectivity in West Antarctica, the eastern Antarctic Peninsula, and along the continental shelf east of Prydz Bay. Connectivity around the shelf is impeded in two main locations, namely, the tip of the Antarctic Peninsula and Cape Adare in the Ross Sea, where significant export of water from the continental shelf is found. These findings help to understand the locations and timescales over which anomalies, such as meltwater from the Antarctic Ice Sheet, can be redistributed downstream.