The Galilean satellites exhibit a monotonic decrease in density (and increase in ice mass fraction) with distance from Jupiter (Pollack & Fanale 1982). Whether this is because of the background conditions when they formed (Lunine & Stevenson 1982; Canup & Ward 2002; Mosqueira & Estrada 2003a; Ronnet et al. 2017), the process of accretion itself (Dwyer et al. 2013), or later loss due to tidal heating (Canup & Ward 2009), has been in dispute for forty years. We find that a hitherto largely neglected process - vapor loss driven by accretional heating (Kuramoto & Matsui 1994) - can reproduce the observed density trend for accretion timescales ≳300 kyr, consistent with gas-starved satellite formation models (Canup & Ward 2002, 2006). In this model both Io and Europa develop an early surface liquid water ocean. Vapor escape from this ocean causes the water inventories of Io and Europa to be completely and mostly lost, respectively. Isotopic fractionation arising from vapor loss means that Europa will develop a higher D/H ratio compared with Ganymede and Callisto. We make predictions that can be tested with in situ measurements of D/H of potential Europa plumes (Roth et al. 2014) by the Europa Clipper spacecraft, or infrared spectroscopic determinations (Clark et al. 2019) of D/H at all three bodies.