We present the final sample of 98 detached double white dwarf (WD) binaries found in the Extremely Low Mass (ELM) Survey, a spectroscopic survey targeting <0.3 M He-core WDs completed in the Sloan Digital Sky Survey footprint. Over the course of the survey we observed ancillary low-mass WD candidates like GD 278, which we show is a P = 0.19 day double WD binary, as well as candidates that turn out to be field blue straggler/subdwarf A-type stars with luminosities too high to be WDs given their Gaia parallaxes. Here, we define a clean sample of ELM WDs that is complete within our target selection and magnitude range 15 < g0 < 20 mag. The measurements are consistent with 100% of ELM WDs being 0.0089 < P < 1.5 day double WD binaries, 35% of which belong to the Galactic halo. We infer that these are mostly He+CO WD binaries given the measurement constraints. The merger rate of the observed He+CO WD binaries exceeds the formation rate of stable mass-transfer AM CVn binaries by a factor of 25, and so the majority of He+CO WD binaries must experience unstable mass transfer and merge. The systems with the shortest periods, such as J0651+2844, are signature LISA verification binaries that can be studied with gravitational waves and light.