The 79° North Glacier (Nioghalvfjerdsbrae, 79NG) is one of three remaining glaciers with a floating tongue in Greenland. Although the glacier has been considered exceptionally stable in the past, earlier studies have shown that the ice tongue has thinned in recent decades. By conducting high-resolution ground-based and airborne radar measurements in conjunction with satellite remote-sensing observations, we find significant changes in the geometry of 79NG. In the vicinity of the grounding line, a 500m high subglacial channel has grown since ~2010 and has caused surface lowering of up to 7.6ma-1. Our results show extreme basal melt rates exceeding 150ma-1 over a period of 17d within a distance of 5km from the grounding line, where the ice has thinned by 32% since 1998. We find a heterogeneous distribution of melt rates, likely due to variability in water column thickness and channelization of the ice base. Time series of melt rates show a decrease in basal melting since 2018, indicating an inflow of colder water into the cavity below 79NG. We discuss the processes that have led to the changes in geometry and conclude that the inflow of warm ocean currents has led to the extensive thinning of 79NG's floating ice tongue near the grounding line over the last 2 decades. In contrast, we hypothesize that the growth of the channel results from increased subglacial discharge due to a considerably enlarged area of summer surface melt due to the warming of the atmosphere.