Quagga mussels have expanded their range across the northern hemisphere in recent decades owing to their dispersal abilities, prolific reproduction rates, and broad ecological tolerances. Their remarkable capacity to filter particulates from the water column has had profound effects on inland aquatic ecosystems. In the North American Great Lakes, quagga mussel populations have increased inexorably since the late 1980's, but it remains unclear whether quagga mussels will follow a similar trajectory in Europe where they have appeared more recently. Here we apply knowledge from a long-term quagga population monitoring effort in the North American lakes to predict future quagga populations in deep European lakes, where quaggas are quickly becoming a conspicuous part of the underwater landscape. We predict that quagga mussel biomass in Lakes Biel, Constance, and Geneva may increase by a factor of 9-20 by 2045. Like in North America, this increase may be characterized by a shift to larger individuals and deeper depths as the population matures. If realized, this rapid expansion of quagga mussels would likely drive the largest aquatic ecosystem change in deep European lakes since the eutrophication period of the mid-20th century.