Background: Explanations for the disproportional COVID-19 burden among immigrants relative to host-country natives include differential exposure to the virus and susceptibility due to poor health conditions. Prior to the pandemic, immigrants displayed deteriorating health with duration of residence that may be associated with increased susceptibility over time. The aim of this study was to compare immigrant–native COVID-19 mortality by immigrants’ duration of residence to examine the role of differential susceptibility. Methods: A population-based cohort study was conducted with individuals between 18 and 100 years old registered in Sweden between 1 January 2015 and 15 June 2022. Cox regression models were run to estimate hazard ratios (HRs) and 95% confidence intervals (CIs). Results: Inequalities in COVID-19 mortality between immigrants and the Swedish-born population in the working-age group were concentrated among those of non-Western origins and from Finland with more than 15 years in Sweden, while for those of retirement age, these groups showed higher COVID-19 mortality HRs regardless of duration of residence. Both age groups of immigrants from Africa and the Middle East showed consistently higher COVID-19 mortality HRs. For the working-age population: Africa: HR<15: 2.46, 95%CI: 1.78, 3.38; HR≥15: 1.49, 95%CI: 1.01, 2.19; and from the Middle East: HR<15: 1.20, 95%CI: 0.90, 1.60; HR≥15: 1.65, 95%CI: 1.32, 2.05. For the retirement-age population: Africa: HR<15: 3.94, 95%CI: 2.85, 5.44; HR≥15: 1.66, 95%CI: 1.32, 2.09; Middle East: HR<15: 3.27, 95%CI: 2.70, 3.97; HR≥15: 2.12, 95%CI: 1.91, 2.34. Conclusions: Differential exposure, as opposed to differential susceptibility, likely accounted for the higher COVID-19 mortality observed among those origins who were disproportionately affected by the pandemic in Sweden.