Leishmaniosis is a high-burden vector-borne disease caused by Leishmania parasites that affect humans and other animals, including dogs and cats. Globalization is one of the main factors that largely contributes to the spread of leishmaniosis to non-endemic areas. A comprehensive review of scientific literature published between 2000 and 2021 was conducted to identify the epidemiological situation and clinical management of imported animal Leishmania infection and leishmaniosis as a fundamental step to better manage individual cases and traveler animal health from a global and One Health perspective. A total of 31 articles were selected, representing 1403 canine, and 25 feline imported cases. Canine and feline leishmanioses in non-endemic areas remain a challenge for veterinarians. Thus, diagnostic and management algorithms for veterinary clinical decision support are proposed. Increased surveillance of non-autochthonous cases, including relocated companion animals, could improve individual health, and mitigate the public and animal health risk of introducing Leishmania species into new areas.