The roles of history, chance and selection have long been debated in evolutionary biology. Though uniform selection is expected to lead to convergent evolution between populations, contrasting histories and chance events might prevent them from attaining the same adaptive state, rendering evolution somewhat unpredictable. The predictability of evolution has been supported by several studies documenting repeatable adaptive radiations and convergence in both nature and laboratory. However, other studies suggest divergence among populations adapting to the same environment. Despite the relevance of this issue, empirical data is lacking for real-time adaptation of sexual populations with deeply divergent histories and ample standing genetic variation across fitness-related traits. Here we analyse the real-time evolutionary dynamics of Drosophila subobscura populations, previously differentiated along the European cline, when colonizing a new common environment. By analysing several life-history, physiological and morphological traits, we show that populations quickly converge to the same adaptive state through different evolutionary paths. In contrast with other studies, all analysed traits fully converged regardless of their association with fitness. Selection was able to erase the signature of history in highly differentiated populations after just a short number of generations, leading to consistent patterns of convergent evolution.