An empirical determination of the f-values of the far-UV Mg II lambda lambda 1239, 1240 lines is reported. The strong near-UV Mg II lambda lambda 2796, 2803 lines are generally highly saturated along most interstellar sight lines outside the local interstellar medium (ISM) and usually yield extremely uncertain estimates of Mg+ column densities in interstellar gas. Since Mg+ is the dominant form of Mg in the neutral ISM, and since Mg is expected to be a significant constituent of interstellar dust grains, the far-UV lines are critical for assessing the role of this important element in the ISM. This study consists of complete component analyses of the absorption along the lines of sight toward HD 93521 in the Galactic halo and xi Persei and zeta Ophiuchi in the Galactic disk, including all four UV Mg+ lines and numerous other transitions. The three analyses yield consistent determinations of the lambda lambda 1239, 1240 f-values, with weighted means of (6.4 +/- 0.4) x 10-4 and (3.2 +/- 0.2) x 10-4, respectively. These results are a factor of ~2.4 larger than a commonly used theoretical estimate, and a factor of ~2 smaller than a recently suggested empirical revision. The effects of this result on gas- and dust-phase abundance measurements of Mg are discussed.