Approximately half of the global population does not have access to the internet, even though digital connectivity can reduce poverty by revolutionizing economic development opportunities. Due to a lack of data, Mobile Network Operators and governments struggle to effectively determine if infrastructure investments are viable, especially in greenfield areas where demand is unknown. This leads to a lack of investment in network infrastructure, resulting in a phenomenon commonly referred to as the `digital divide`. In this paper we present a machine learning method that uses publicly available satellite imagery to predict telecoms demand metrics, including cell phone adoption and spending on mobile services, and apply the method to Malawi and Ethiopia. Our predictive machine learning approach consistently outperforms baseline models which use population density or nightlight luminosity, with an improvement in data variance prediction of at least 40%. The method is a starting point for developing more sophisticated predictive models of infrastructure demand using machine learning and publicly available satellite imagery. The evidence produced can help to better inform infrastructure investment and policy decisions.