Mycobacterium abscessus, a multidrug-resistant nontuberculous mycobacterium, has emerged as a major pathogen affecting people with cystic fibrosis (CF). Although originally thought to be acquired independently from the environment, most individuals are infected with one of several dominant circulating clones (DCCs), indicating the presence of global transmission networks of M. abscessus. How and when these clones emerged and spread globally is unclear. Here, we use evolutionary analyses of isolates from individuals both with and without CF to reconstruct the population history, spatiotemporal spread and recent transmission networks of the DCCs. We demonstrate synchronous expansion of six unrelated DCCs in the 1960s, a period associated with major changes in CF care and survival. Each of these clones has spread globally as a result of rare intercontinental transmission events. We show that the DCCs, but not environmentally acquired isolates, exhibit a specific smoking-associated mutational signature and that current transmission networks include individuals both with and without CF. We therefore propose that the DCCs initially emerged in non-CF populations but were then amplified and spread through the CF community. While individuals with CF are probably the most permissive host, non-CF individuals continue to play a key role in transmission networks and may facilitate long-distance transmission.