Washington actually had several sets of false teeth, made of different materials (not wood) and were probably made by different people. Some of them were certainly made by his dentist of many years, John Greenwood of New York.
According to myth it was Paul Revere. Dr John Greenwood of New York City about 1785 did George Washington's porcelain teeth. Dr Greenwood also invented the foot power drill but the question was "according to myth."