We have built a high-accuracy wavelength meter for tunable lasers using a scanning Michelson interferometer and a reference laser of known wavelength. The reference laser is a frequency-stabilized diode laser locked to an atomic transition in Rb. The wavemeter has a statistical error per measurement of 5 parts in 107, which can be reduced considerably by averaging. Using a second stabilized diode laser, we have verified that systematic errors are below 4 parts in 108.