Probabilistic Tsunami Hazard Assessment (PTHA) is the essential first step for quantifying the long-term risk posed by landslide-generated tsunamis at active volcanic islands like Stromboli, Italy. This study presents a first PTHA for Stromboli, providing a quantitative and transparent basis for risk mitigation and long-term coastal planning at Stromboli. In particular, our work integrates two new databases of numerical simulations for volcanic landslide-induced tsunamis with occurrence probabilities derived from expert elicitation (described in the companion paper by Tadini et al., submitted). We introduce a new methodology to translate elicited probabilities for landslide frequency, volume, and location into a full suite of probabilistic hazard products. The results, expressed as hazard curves, maps and profiles (5^th, 50^th and 95^th percentiles), are presented for alternative modelling setups, including different high-resolution topobathymetric models and code versions, to transparently account for epistemic uncertainty in the numerical hazard assessment. Our findings quantify a significant tsunami hazard for Stromboli's inhabited coastal areas over the next 50 years. The 95^th percentile maps indicate that inundation by at least 0.5 m of water has >90 % to occur along coast of Stromboli village the over the next 50 years. Furthermore, the hazard curves at critical sites show non-negligible probabilities of exceeding severe inundation depths in the same 50 years temporal frame.