Probe measurements of electrostatic plasma fluctuations in the scrape-off layer (SOL) of the TCV tokamak are compared with the results from two-dimensional interchange turbulence simulations. Excellent agreement is found for both the radial variation of statistical moments and temporal correlations, clearly indicating that turbulent transport in the tokamak SOL is due to radial advection of blob-like filamentary structures. This offers an explanation both for the basic mechanism driving the anomalous SOL particle transport and the now commonly observed broad particle density profiles, extending deep into the SOL and thought to be the cause of high levels of main chamber plasma-wall interactions.