Calculating the galaxy merger rate requires both a census of galaxies identified as merger candidates, and a cosmologically-averaged `observability timescale T_obs(z) for identifying galaxy mergers. While many have counted galaxy mergers using a variety of techniques, T_obs(z) for these techniques have been poorly constrained. We address this problem by calibrating three merger rate estimators with a suite of hydrodynamic merger simulations and three galaxy formation models. We estimate T_obs(z) for (1) close galaxy pairs with a range of projected separations, (2) the morphology indicator G-M20, and (3) the morphology indicator asymmetry A. Then we apply these timescales to the observed merger fractions at z < 1.5 from the recent literature. When our physically-motivated timescales are adopted, the observed galaxy merger rates become largely consistent. The remaining differences between the galaxy merger rates are explained by the differences in the range of mass-ratio measured by different techniques and differing parent galaxy selection. The major merger rate per unit co-moving volume for samples selected with constant number density evolves much more strongly with redshift (~ (1+z)^(+3.0 pm 1.1)) than samples selected with constant stellar mass or passively evolving luminosity (~ (1+z)^(+0.1 pm 0.4)). We calculate the minor merger rate (1:4 < M_{sat}/M_{primary} <~ 1:10) by subtracting the major merger rate from close pairs from the `total merger rate determined by G-M20. The implied minor merger rate is ~3 times the major merger rate at z ~ 0.7, and shows little evolution with redshift.
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