We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have analyzed Global Oscillation Network Group (GONG) Dopplergrams with a ring-diagram analysis covering about 15 years and Helioseismic and Magnetic Imager (HMI) Dopplergrams covering more than 6 years. After subtracting the average rotation rate and meridional flow, we have calculated the divergence of the horizontal residual flows from the maximum of Solar Cycle 23 through the declining phase of Cycle 24. The subsurface flows are mainly divergent at quiet regions and convergent at locations of high magnetic activity. The relationship is essentially linear between divergence and magnetic activity at all activity levels at depths shallower than about 10 Mm. At greater depths, the relationship changes sign at locations of high activity; the flows are increasingly divergent at locations with a magnetic activity index (MAI) greater than about 24 G. The flows are more convergent by about a factor of two during the rising phase of Cycle 24 than during the declining phase of Cycle 23 at locations of medium and high activity (about 10 to 40 G MAI) from the surface to at least 10 Mm. The subsurface divergence pattern of Solar Cycle 24 first appears during the declining phase of Cycle 23 and is present during the extended minimum. It appears several years before the magnetic pattern of the new cycle is noticeable in synoptic maps. Using linear regression, we estimate the amount of magnetic activity that would be required to generate the precursor pattern and find that it should be almost twice the amount of activity that is observed.