Abstract Magnetic field draping occurs when the magnetic field lines frozen in a plasma flow wrap around a body or plasma environment. The draping of the interplanetary magnetic field (IMF) around the Earth’s magnetosphere has been confirmed in the early days of space exploration. However, its global and three‐dimensional structure is known from modeling only, mostly numerical. Here, this structure in the dayside of the Earth’s magnetosheath is determined as a function of the upstream IMF orientation purely from in‐situ spacecraft observations. We show the draping structure can be organized in three regimes depending on how radial the upstream IMF is. Quantitative analysis demonstrates how the draping pattern results from the magnetic field being frozen in the magnetosheath flow, deflected around the magnetopause. The role of the flow is emphasized by a comparison of the draping structure to that predicted to a magnetostatic draping.