The most striking feature of the Sun's magnetic field is its cyclic behaviour. The number of sunspots, which are dark regions of strong magnetic field on the Sun's surface, varies with a period of about 11 years. Superposed on this cycle are secular changes that occur on timescales of centuries and events like the Maunder minimum in the second half of the seventeenth century, when there were very few sunspots. A part of the Sun's magnetic field reaches out from the surface into interplanetary space, and it was recently discovered that the average strength of this interplanetary field has doubled in the past 100 years. There has hitherto been no clear explanation for this doubling. Here we present a model describing the long-term evolution of the Sun's large-scale magnetic field, which reproduces the doubling of the interplanetary field. The model indicates that there is a direct connection between the length of the sunspot cycle and the secular variations.