The aim of the paper is to propose the construction of an index that captures the economic complexity of cities over the globe, as well as to explore whether it is a good predictor for a range of city-level economic outcomes. This index aspires to mitigate data scarcity for cities and to provide policy makers with the tools for monitoring the evolving role of cities in the global economy. Analytically, we implement the economic complexity methodology on data for the ownership, location and economic activities of the world's 3,000 largest firms and their subsidiaries to propose a new indicator that quantifies the network of the largest cities worldwide and the economic activities of their globalized firms. We first show that complex cities are the highly diversified cities that host non-ubiquitous economic activities of firms with global presence. Then, in a sample of EU cities, we show that complex cities tend to be more prosperous, have higher population, and are associated with more jobs, human capital, innovation, technology and transport infrastructure. Last, using OLS methodology and accounting for several other confounders, we show that a higher ECI, at the city level, enhances the resilience of cities to negative economic shocks, i.e., their ability to bounce back after a shock. Specifically, we find that the expected increase of the ratio of employment in 2012 over 2006 is 0.01 (mean: 0.992; standard deviation: 0.081) when the ECI increases by 1 unit (mean: 0.371; standard deviation: 1.094), i.e., a satisfactory pace of recovery, in terms of employment. The ability to diversify in the presence of a shock, the reallocation of factors of production to other sectors and the ability to extract rents associated with those diversified activities, uncovers the mechanics of the ECI index.