The central complex is a highly conserved insect brain region composed of morphologically stereotyped neurons that arborize in distinctively shaped substructures. The region has been implicated in a wide range of behaviors, including navigation, motor control and sleep, and has been the subject of several modeling studies exploring its circuit computations. Most studies so far have relied on assumptions about connectivity between neurons in the region based on their overlap in light-level microscopic images. Here, we present an extensive functional connectome of Drosophila melanogaster's central complex at cell-type resolution. Using simultaneous optogenetic stimulation, GCaMP recordings and pharmacology, we tested the connectivity between over 70 presynaptic-to-postsynaptic cell-type pairs. The results reveal a range of inputs to the central complex, some of which have not been previously described, and suggest that the central complex has a limited number of output channels. Additionally, despite the high degree of recurrence in the circuit, network connectivity appears to be sparser than anticipated from light-level images. Finally, the connectivity matrix we obtained highlights the potentially critical role of a class of bottleneck interneurons of the protocerebral bridge known as the Δ7 neurons. All data is provided for interactive exploration in a website with the capacity to accommodate additional connectivity information as it becomes available. Raw data and code are made available as an OpenScienceFramework project.