Fire is a major disturbance driving the dynamics of the world's savannas. Almost all fires are set by humans who are increasingly altering fire timing and frequency on every continent. The world's largest protected areas of savannas are found in monsoonal northern Australia. These include relatively intact, tall, open forests where traditional indigenous fire regimes have been largely replaced in the past half century by contemporary patterns with trees experiencing fire as often as three out of five years. Eucalypt canopy trees form the basic structure of these savannas and changes to the canopy due to fire regimes cascade to affect other plants and animals. In this study, we used data from nearly three decades of field studies on the effects of fire on individual trees to define eight life‐history stages and to calculate transition rates among stages. We developed a stage‐based matrix population model that explicitly considers how fire season and understory influence growth, survival, and recruitment for each life‐history stage. Long‐term population growth rates and transient population dynamics were calculated under five different fire regimes, each in two understory types, using both deterministic and stochastic simulations of seasonal timing of fires. We found that fire was necessary for long‐term persistence of eucalypt canopy tree populations but, under annual fires, most populations did not survive. Population persistence was highly dependent on fire regime (fire season and frequency) and understory type. A stochastic model tended to yield higher population growth rates than the deterministic model with regular, periodic fires, even under the same long‐term frequency of fires. Transient population dynamics over 100 yr also depended on fire regime and understory, with implications for savanna physiognomy and management. Model predictions were tested in an independent data set from a 21‐yr longitudinal field study in Kakadu National Park. This study is a novel and integrative contribution to our understanding of fire in savanna biomes regarding the potential for long‐term persistence and transient dynamics of savanna canopy tree populations. The model is relatively simple, generalizable, and adaptable for further investigations of the population dynamics of savanna trees under fire.