Over 400,000 people across the Americas are thought to have been infected with Zika virus as a consequence of the 2015-2016 Latin American outbreak. Official government-led case count data in Latin America are typically delayed by several weeks, making it difficult to track the disease in a timely manner. Thus, timely disease tracking systems are needed to design and assess interventions to mitigate disease transmission. We combined information from Zika-related Google searches, Twitter microblogs, and the HealthMap digital surveillance system with historical Zika suspected case counts to track and predict estimates of suspected weekly Zika cases during the 2015-2016 Latin American outbreak, up to three weeks ahead of the publication of official case data. We evaluated the predictive power of these data and used a dynamic multivariable approach to retrospectively produce predictions of weekly suspected cases for five countries: Colombia, El Salvador, Honduras, Venezuela, and Martinique. Models that combined Google (and Twitter data where available) with autoregressive information showed the best out-of-sample predictive accuracy for 1-week ahead predictions, whereas models that used only Google and Twitter typically performed best for 2- and 3-week ahead predictions. Given the significant delay in the release of official government-reported Zika case counts, we show that these Internet-based data streams can be used as timely and complementary ways to assess the dynamics of the outbreak.