Rising global food demands have led to unprecedented aquaculture growth. Aquaculture has simultaneously become a major global pathway for biological invasions. Non-native farmed species, while highly productive, can undermine sustainability agendas because of their environmental and socio-economic damages when they escape. We analyse global non-native production among farmed species and quantify monetary biological invasion costs. Globally, one third of the 544 species used in aquaculture have been farmed in their non-native range, totalling 539 million tonnes with an economic value of USD 1.1 trillion. Algae and fishes dominated non-native production, but non-native crustacean production grew fastest (>3000% since 2000, compared to the preceding 20 years). The 25 non-native farmed species with reported monetary costs have caused up to USD 10 billion costs globally. To address the rising threats of biological invasions triggered by aquaculture escapees, a paradigm shift by enhancing biosecurity and promoting sustainable use of native resources is needed.