Aim: The drivers and dynamics of initial human migrations across individual islands and archipelagos are poorly understood, affecting assessments of human-modification of island biodiversity. Here, we describe and test a process-explicit approach for reconstructing human arrival and expansion on islands, which combines archaeological and climate records with high-resolution spatial population models. Using Polynesian colonisation of New Zealand as an example, we show that our new method can generate information crucial for assessing how humans affected biodiversity on islands. Innovation: The transition of islands from prehuman to human dominated ecosystems has typically been assessed by comparing biodiversity before and after time of first arrival, without considering the potential importance of the spatiotemporal dynamics of the human expansion event. Our new approach, which uses pattern-oriented modelling methods to combine inferences of human colonisation dynamics from dated archaeological material with spatially explicit population models, produces validated reconstructions of the pattern and pace of human migration across islands at high spatiotemporal resolutions. From these reconstructions, demographic and environmental drivers of human colonization can be identified, and the role that people had on biodiversity established. Using this technique, we show that closely reconciling inferences of Polynesian colonisation of New Zealand requires there to have been a single founding population of approximately 500 people, arriving between 1233 and 1257 AD, settling multiple areas, and expanding quickly over both North and South islands. The resultant maps of Māori colonisation dynamics provide new opportunities to better determine how human activities transformed biodiversity of New Zealand in space and time. Main conclusions: Process-explicit models can reconstruct human migration across large islands, producing validated, high resolution spatiotemporal projections of human occupancy and abundance that account for dispersal and population dynamics. This modelling framework should prove effective across any islands and archipelagos where climate and archaeological records are available.