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The young pulsar PSR B1828-11 has long been known to show correlated shape and spindown changes with time-scales of roughly 500 and 250 d, perhaps associated with large-scale magnetospheric switching. Here, we present multihour observations with the Parkes and Green Bank Telescopes at multiple phases across the 500-d cycle and show that the pulsar undergoes mode-changing between two stable, extreme profile states. The fraction of time spent in each profile state naturally accounts for the observed overall 'shape parameter' (defined to be 0 for wide profiles and 1 for narrow ones); this and the variable rate of the mode transitions are directly related to the spindown changes. We observe that the mode transition rate could plausibly function as an additional parameter governing the chaotic behaviour in this object which was proposed earlier by Seymour and Lorimer. Free precession is not needed to account for the variations.