Urban form in both two-(2D) and three-dimensions (3D) has significant impacts on local and global environments. Here we developed the largest global dataset characterizing 2D and 3D urban growth for 478 cities with populations of one million or larger. Using remote sensing data from the SeaWinds scatterometer for 2001 and 2009, and the Global Human Settlement Layer for 2000 and 2014, we applied a cluster analysis and found five urban growth typologies: stabilized, outward, mature upward, budding outward, upward and outward. Budding outward is the dominant typology worldwide, per the largest total area. Cities characterized by upward and outward growth are few in number and concentrated primarily in China and South Korea, where there has been a large increase in high-rises during the study period. With the exception of East Asia, cities within a geographic region exhibit remarkably similar patterns of urban growth. Our results show that every city exhibits multiple urban growth typologies concurrently. Thus, while it is possible to describe a city by its dominant urban growth typology, a more accurate and comprehensive characterization would include some combination of the five typologies. The implications of the results for urban sustainability are multifold. First, the results suggest that there is considerable opportunity to shape future patterns of urbanization, given that most of the new urban growth is nascent and low magnitude outward expansion. Second, the clear geographic patterns and wide variations in the physical form of urban growth, within country and city, suggest that markets, national and subnational policies, including the absence of, can shape how cities grow. Third, the presence of different typologies within each city suggests the need for differentiated strategies for different parts of a single city. Finally, the new urban forms revealed in this analysis provide a first glimpse into the carbon lock-in of recently constructed energy-demanding infrastructure of urban settlements.