Sub-Saharan Africa (SSA) is one of the regions with the highest coverage gaps (number of people uncovered by mobile signal). Providing universal coverage is key to unlocking the economic potential of such regions and even addressing second order effects such as poverty and inequality. However, addressing coverage gaps requires detailed knowledge of the population number and distribution to design effective and sustainable broadband solutions. To this end, this dissertation presents three open-source techno-economic geospatial models for addressing the connectivity challenges in SSA. The model is a framework of evaluating the number of people uncovered by mobile broadband and living below the poverty line in areas of different population density thresholds (deciles 1 to 10). The model is applied to assess the viability of three broadband technologies (mobile, fixed fiber and satellites) in connecting 16 million people who are living below US$ 1.9 a day and uncovered by 3G cellular signal. A demand model for quantifying the unconnected and poor population is first presented. It is estimated that over 225 million people in 44 SSA countries are living below US$ 1.9 a day in areas with a population density of less than 106 people per km2. A mobile broadband model is thus developed to compare the capacity, cost and Greenhouse Gas (GHG) environmental emissions due to deployment and operations of the system in connecting the unconnected population. An innovative low-cost fixed fiber architecture is also designed to bring fiber close to areas inhabited by 550 million people (48% of the total SSA population). Using the Geographical Information Systems (GIS) spatial optimization approach, two algorithms are presented. The Minimum Spanning Tree (MST) and Prize-Collecting Steiner Tree (PCST) algorithms are used to design the least-cost fixed fiber network closer to the settlements before quantifying the cost and resultant environmental impacts. The results revealed that it will cost US$ 26-67 billion (3.3% of SSA GDP) to bring fiber closer to the population living in areas with over 106 people per km2. Furthermore, deployment of fiber closer to people in these areas will result in 3.1-20 Mt CO2 e (2.4% of the total greenhouse gas emissions in SSA). In addition to mobile and fixed fiber broadband, the study assessed the viability of Low Earth Orbit (LEO) satellite systems. Three LEO systems (Starlink, OneWeb and Kuiper) were assessed to determine the average capacity, cost and GHG emissions per-user due to launching the satellites in space to serve the frontier population especially in areas with a population density of less than 21 people per km2. The results show that LEO constellations provide substantial improvement in speed requirements for rural and remote communities (decile 9 and 10). For instance, in decile 10 (less than 9 people per km²), the average per-user capacity values are 35 Mbps (Starlink), 16 Mbps (OneWeb), and 35 Mbps (Kuiper). However, this comes at a price, as the emissions from the LEO systems are considerably high compared to when the areas are served by terrestrial 4G mobile networks. On a global scale, phase 1 LEO systems have an operational carbon footprint of 0.2-0.7 Mt CO2 e. This is equivalent to emissions from 43-150k annual gasoline-powered passenger vehicles.