Community assembly is central to ecology, yet ecologists have amassed little quantitative information about how food webs assemble. Theory holds that colonisation rate is a primary driver of community assembly. We present new data from a mesocosm experiment to test the hypothesis that colonisation rate also determines the assembly dynamics of food webs. By manipulating colonisation rate and measuring webs through time, we show how colonisation rate governs structural changes during assembly. Webs experiencing different colonisation rates had stable topologies despite significant species turnover, suggesting that some features of network architecture emerge early and change little through assembly. But webs experiencing low colonisation rates showed less variation in the magnitudes of trophic fluxes, and were less likely to develop coupled fast and slow resource channels - a common feature of published webs. Our results reveal that food web structure develops according to repeatable trajectories that are strongly influenced by colonisation rate.