The dense outflow through Denmark Strait is the largest contributor to the lower limb of the Atlantic Meridional Overturning Circulation, yet a description of the full velocity field across the strait remains incomplete. Here we analyze a set of 22 shipboard hydrographic/velocity sections occupied along the Látrabjarg transect at the Denmark Strait sill, obtained over the time period 1993–2018. The sections provide the first complete view of the kinematic components at the sill: the shelfbreak East Greenland Current (EGC), the combined flow of the separated EGC and the North Icelandic Jet (NIJ), and the northward flowing North Icelandic Irminger Current (NIIC). The total mean transport of overflow water is 3.54 ± 0.29 Sv, comparable to previous estimates. The dense overflow is partitioned in terms of water mass constituents and flow components. The mean transports of the two types of overflow water – Atlantic-origin Overflow Water and Arctic-origin Overflow Water – are comparable in Denmark Strait, while the merged NIJ/separated EGC transports 55% more water than the shelfbreak EGC. A significant degree of water mass exchange takes place between the branches as they converge in Denmark Strait. There are two dominant time-varying configurations of the flow that are characterized as a cyclonic state and a non-cyclonic state. These appear to be wind-driven. A potential vorticity analysis indicates that the flow through Denmark Strait is subject to symmetric instability. This occurs at the top of the overflow layer, implying that the mixing/entrainment process that modifies the overflow water begins at the sill.