Towards the end of an infectious disease outbreak, when a period has elapsed without new case notifications, a key question for public health policymakers is whether the outbreak can be declared over. This requires the benefits of a declaration (e.g. relaxation of outbreak control measures) to be balanced against the risk of a resurgence in cases. To support this decision-making, mathematical methods have been developed to quantify the end-of-outbreak probability. Here, we propose a new approach to this problem that accounts for a range of features of real-world outbreaks, specifically: (i) incomplete case ascertainment, (ii) reporting delays, (iii) individual heterogeneity in transmissibility and (iv) whether cases were imported or infected locally. We showcase our approach using two case studies: Covid-19 in New Zealand in 2020 and Ebola virus disease in the Democratic Republic of the Congo in 2018. In these examples, we found that the date when the estimated probability of no future infections reached 95% was relatively consistent across a range of modelling assumptions. This suggests that our modelling framework can generate robust quantitative estimates that can be used by policy advisors, alongside other sources of evidence, to inform end-of-outbreak declarations.