One of the major limitations that hinder widespread application of biodiesel in automotive engines is its poor oxidative stability, which in turn depends upon methyl ester constituents of biodiesel as well the storage conditions. Hence, a relative assessment of the oxidative stability of biodiesels across the different parts of the world is rather difficult. In the present work, oxidative stability of biodiesel based on the ASTM D4625 accelerated oxidative stability test is compared with that of gradual oxidation under two different long-term storage conditions, namely, open to air and sunlight and closed to air and sunlight. Neat Karanja biodiesel and its blends with diesel at 25, 50, and 75% by volume are used for the present study. The important physicochemical properties of fuel samples are measured at regular time intervals to evaluate the rate of oxidation and the extent of fuel quality degradation. The results obtained show that neat Karanja biodiesel stored under open to air and sunlight conditions has the highest rate of oxidation and fuel quality degradation with a 32% increase in kinematic viscosity, 1.5% increase in density, and 3% decrease in calorific value. The acid value of all the tested fuel samples increased beyond ASTM and EN standard specification limits within the first 3 months of storage period. The peroxide value showed a steep increase during the first 6 months of storage period and decreased afterward. The effects of adding the TBHQ antioxidant in Karanja biodiesel at varying concentrations are also evaluated based on the measured Rancimat induction period, and it is observed that 250 ppm TBHQ is required to meet EN 41214 standard specifications for biodiesel. No correlations are found to exist between the properties of fuel samples stored under gradual and accelerated oxidation conditions. However, adopting the ASTM D4625 standard test method to evaluate the storage stability of biodiesel avoids any ambiguity owing to the variations in the storage and the ambient conditions across the different parts of the world.