Climate variability and climate change influence human migration both directly and indirectly through a variety of channels that are controlled by individual and household socioeconomic, cultural, and psychological processes as well as public policies and network effects. Characterizing and predicting migration flows are thus extremely complex and challenging. Among the quantitative methods available for predicting such flows is the widely used gravity model that ignores the network autocorrelation among flows and thus may lead to biased estimation of the climate effects of interest. In this study, we use a network model, the additive and multiplicative effects model for network (AMEN), to investigate the effects of climate variability, migrant networks, and their interactions on South African internal migration. Our results indicate that prior migrant networks have a significant influence on migration and can modify the association between climate variability and migration flows. We also reveal an otherwise obscure difference in responses to these effects between migrants moving to urban and non-urban destinations. With different metrics, we discover diverse drought effects on these migrants; for example, the negative standardized precipitation index (SPI) with a timescale of 12 months affects the non-urban-oriented migrants’ destination choices more than the rainy season rainfall deficit or soil moisture do. Moreover, we find that socioeconomic factors such as the unemployment rate are more significant to urban-oriented migrants, while some unobserved factors, possibly including the abolition of apartheid policies, appear to be more important to non-urban-oriented migrants.