Rapid and affordable methods of testing for COVID-19 infections are essential to reduce infection rates and prevent medical facilities from becoming overwhelmed. Current approaches of detecting COVID-19 require in-person testing with expensive kits that are not always easily accessible. This study demonstrates that crowdsourced cough audio samples recorded and acquired on smartphones from around the world can be used to develop an AI-based method that accurately predicts COVID-19 infection with an ROC-AUC of 77.1% (75.2%-78.3%). Furthermore, we show that our method is able to generalize to crowdsourced audio samples from Latin America and clinical samples from South Asia, without further training using the specific samples from those regions. As more crowdsourced data is collected, further development can be implemented using various respiratory audio samples to create a cough analysis-based machine learning (ML) solution for COVID-19 detection that can likely generalize globally to all demographic groups in both clinical and non-clinical settings.