Centrosome amplification results into genetic instability and predisposes cells to neoplastic transformation. Supernumerary centrosomes trigger p53 stabilization dependent on the PIDDosome (a multiprotein complex composed by PIDD1, RAIDD and Caspase‐2), whose activation results in cleavage of p53’s key inhibitor, MDM2. Here, we demonstrate that PIDD1 is recruited to mature centrosomes by the centriolar distal appendage protein ANKRD26. PIDDosome‐dependent Caspase‐2 activation requires not only PIDD1 centrosomal localization, but also its autoproteolysis. Following cytokinesis failure, supernumerary centrosomes form clusters, which appear to be necessary for PIDDosome activation. In addition, in the context of DNA damage, activation of the complex results from a p53‐dependent elevation of PIDD1 levels independently of centrosome amplification. We propose that PIDDosome activation can in both cases be promoted by an ANKRD26‐dependent local increase in PIDD1 concentration close to the centrosome. Collectively, these findings provide a paradigm for how centrosomes can contribute to cell fate determination by igniting a signalling cascade. SYNOPSIS The PIDDosome is a Caspase‐2‐activating platform assembling in response to two stimuli: genotoxic stress and supernumerary centrosomes. Here, both triggers are shown to rely on centrosomal localization of PIDD1, highlighting the centrosome’s capability to influence cell fate. Centriolar distal appendage protein ANKRD26 is the centrosomal PIDD1 receptor. The centrosome recruits the PIDD1 precursor, which undergoes subsequent autoproteolysis. Clustering of PIDD1‐positive extra‐centrosomes is required for PIDDosome activation. P53‐dependent PIDD1 transactivation leads to centrosome‐dependent PIDDosome activation even in the absence of extra‐centrosomes. ANKRD26‐dependent PIDD1 recruitment is involved in p53 activation both upon genotoxic stress and in the presence of supernumerary centrosomes.