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Well-constrained earthquake depth estimations are important for seismic hazard determination. As local networks of the East-African Rift are usually too sparse for reliable depth estimations, we used detections of pP and sP phase arrivals (the so-called depth phases) at teleseismic distance to constrain earthquake depths in this region. We rely on a fully automatic Cepstral analysis approach, first validated at the global scale using the ISC-EHB catalogue, then applied on the East-African seismicity. We investigated 9575 earthquakes from magnitude 2 since 2005 which allows us to constrain the depth estimation of 584 events with magnitude mainly above 3.5, complemented by 139 reliable depth estimations from previous studies based on teleseismic data as well. To ensure a final catalogue as complete as possible, we also identified from regional catalogues 113 earthquakes assumed to be well constrained, based on network geometry empirical criteria. Thanks to this study, we finally propose new earthquake depth distributions for the seismic source zonation defined by Poggi et al. in order to estimate the seismic hazard of the East African Rift region. Including those new distributions in the source models leads to significant changes of seismic hazard assessments results. [ABSTRACT FROM AUTHOR]