Macronutrient composition of the diet influences the development of obesity and insulin resistance. The aim of this study was to assess the role of dietary fat quantity and fatty acid composition in body composition, insulin resistance, and insulin secretion. An open parallel randomized trial design was used. Overweight participants (n = 75) were randomized to follow a low-fat vegan (n = 38) or control diet (n = 37) for 16 weeks. Dual X-ray absorptiometry was used to measure body composition. Insulin resistance was assessed with the Homeostasis Model Assessment (HOMA-IR) index. Insulin secretion was assessed after stimulation with a liquid breakfast (Boost Plus, Nestle, Vevey, Switzerland). Self-reported 3-day diet records were used to assess dietary intake. A linear regression model was used to test the relationship between fat intake and body composition, insulin resistance, and insulin secretion. Changes in fat intake expressed as percent of total energy consumed correlated positively with changes in fat mass (r = 0.52; p < 0.001; and 0.347; p = 0.006, respectively), even after adjustment for changes in body-mass index (BMI) and energy intake (0.33; p = 0.01). Decreased intakes of C18:0 (r = 0.37, p = 0.004) and CLA-trans-10-cis12 (r = 0.40, p = 0.002), but increased intake of C18:2 (r = −0.40, p = 0.002) and C18:3 (p = −0.36, p = 0.006), were associated with a decrease in HOMA-IR, independent on changes in BMI and energy intake. The main fatty acids associated with changes in fasting insulin secretion were C12:0 (r = −0.31, p = 0.03), and TRANS 16:1 (r = −0.33, p = 0.02), both independent on changes in BMI and energy intake. Our findings demonstrate that, in the context of a low-fat vegan diet, decreased intake of saturated and trans fats and increased relative content of polyunsaturated fatty acids, particularly linoleic and α-linolenic acids, are associated with decreased fat mass and insulin resistance, and enhanced insulin secretion.