The impact of a large extraterrestrial object on the Earth can produce a geomagnetic reversal through the following mechanism: dust from the impact center and soot from fires trigger a climate change and the beginning of a little ice age. The redistribution of water near the equator to ice at high latitudes alters the rotation rate of the crust and mantle of the Earth. If the sea-level change is sufficiently large (>10 meters) and rapid (in a few hundred years), then the velocity shear in the liquid core disrupts the convective cells that subsequently form distort and tangle the previous field, reducing the dipole component near to zero while increasing the energy in multipole components. Eventually a dipole is rebuilt by dynamo action, and the event is seen either as a geomagnetic reversal or as an excursion. Sudden climate changes from other causes such as volcanic eruptions could also trigger reversals. This mechanism may not be the sole cause of geomagnetic reversals, but it can account for the rapid drop of the dipole component preceding a reversal, the predominance of multipole components during a transition, the associations of microtektites, temperature drops and extinctions with reversals, and the possible correlation between peaks in the geomagnetic reversal rate and the times of mass extinctions. The model may also account for the long-term changes in the average rate of reversals. We make several testable predictions.