Global warming is expected to lead to a substantial rise in coastal sea levels by the end of the century, which imposes future impacts and adaptation challenges on the coastal zone. Capturing the socio-economic costs of sea level rise (SLR) is therefore an important component of climate impacts in integrated assessment models (IAMs). However, there is a lack of process-based models of SLR impacts with a focus on global, time-varying dynamics. Current SLR impact models often follow a cost-benefit analysis approach, fail to represent diverse pathways of SLR impacts, or do not include coastal adaptation. Here, we present the Feedback-based knowledge Repository for Integrated assessments of Sea level rise Impacts and Adaptation version 1.0 (FRISIAv1.0), a model designed for process-based, non-equilibrium IAMs that follows a system dynamics approach. FRISIA's SLR component is based on existing models of SLR, while its impact component is a substantially modified adaptation of the Coastal Impact and Adaptation Model (CIAM) for use in globally or regionally aggregated models. While a reduced-feedback version of FRISIA approximately reproduces CIAM results, the integration of additional feedbacks in FRISIA leads to emerging new behaviours, such as a potential peak and decline in SLR-driven storm surge damages in the early 22^nd century, due to economic feedbacks in the coastal zone. When coupling FRISIA to an IAM, global GDP is reduced by 1.6–6.1 % (17^th–83^rd percentile range) under a global SLR of 0.8 m by 2100 and no coastal adaptation, which is in the range of previous studies. The coupling of a diverse set of SLR impact streams from FRISIA into a system dynamics IAM has the advantage of leading to a wide range of socio-economic consequences that go beyond just a reduction in global GDP, such as an effect on inflation. Our simulations highlight the benefits of accounting for dynamic coastal feedback and coupling diverse SLR impact and cost strains to IAMs, and showcase that FRISIAv1.0 is a useful tool for doing so.