In this paper, we examine the electrification of the heating sector as a decarbonisation strategy, discuss its effectiveness, and preliminary assess its impact on the European power system. For this purpose, we perform a complete description of the EU heating sector compliant with official statistics and decompose the EU power demand in different uses to define and assess different levels of heat electrification. We find that heat electrification is an effective decarbonisation option, which can reduce the total energy related emissions by up to 17%, if paired with simultaneous expansion of low-carbon energy. Due to the relative sizes of heat and power demands, we find that most national power systems could cope with higher heat-electrification rates. Specifically, an additional heat pump capacity in the order of 1.1–1.6 TWth can be deployed based on the existing firm power capacity, which would correspond to a heat pump share of 29–45% in space heating. Based on their current power capacity, 12 Member States are prepared for even full electrification scenarios, whereas three Member States could get their power system stressed if 40–60% of all fossil-fuelled technologies are substituted. Flexible electric demand is identified as a key enabler of larger heat electrification shares.