Amino acids tyrosine (Tyr) and tryptophan (Trp) play a significant role in the regulation of energy metabolism, locomotor activity, and eating behavior. We studied the possibility of modulating these processes in obesity by increasing the pool of Tyr and Trp in the experimental diet. As a model of obesity, we used Wistar rats fed a diet with an excess specific energy value (HFCD) for 64 days. Trp led to a normalization of the rats’ body weight almost to the control level, but increased anxiety-like behavior and decreased long-term memory. The consumption of amino acids resulted in increased grip strength and impairment of short-term memory. The locomotor activity of animals decreased with age as a result of Tyr consumption, while Trp, on the contrary, prevented this. The Tyr supplementation led to the normalization of triglycerides and LDL. In the spleen cell lysates, amino acids suppressed the production of proinflammatory cytokines. The liver tissue morphology showed that the consumption of Tyr noticeably weakened the signs of fatty degeneration. The addition of Trp, on the contrary, led to an unfavorable effect, consisting of the appearance of a high number of large rounded fatty vacuoles. The data obtained indicate a more pronounced anti-inflammatory effect of Tyr as compared to Trp.