We show that the variations of the interplanetary magnetic field strength (B) over a 22-year period are tracked by the inverted profile of the cosmic ray density measured by neutron monitors. We suggest that global changes in the Sun's magnetic field are more important for long-term modulation than magnetic field enhancements resulting from the merging of high-speed flows and coronal mass ejections in the outer heliosphere. The unexpectedly close relationship that we find between the “tilt angle” of the heliospheric current sheet and the cosmic ray density away from solar minimum for both polarity states of the solar magnetic field may be accounted for by the anticorrelation between the cosmic ray density and field strength variations.