(1) Background: The elderly suffer from functional constipation (FC), whose causes are not fully known, but nutritional factors may play a role. The aim of the present study was to assess the effect of a low FODMAP diet supplemented with L-tryptophan (TRP) on its metabolism and symptoms of functional constipation in elderly patients. (2) Methods: This study included 40 people without abdominal complaints (Group I, controls) and 60 patients with FC, diagnosed according to the Rome IV Criteria (Group II). Two groups were randomly selected: Group IIA (n = 30) was qualified for administration of the low FODMAP diet, and the diet of patients of Group IIB (n = 30) was supplemented with 1000 mg TRP per day. The severity of abdominal symptoms was assessed with an abdominal pain index ranging from 1 to 7 points (S-score). The concentration of TRP and its metabolites, 5-hydroxyindoleacetic acid (5-HIAA), kynurenine (KYN), and 3-indoxyl sulfate (3-IS) in urine were determined using the LC-MS/MS method. (3) Results: In Group II, 5-HIAA concentration in urine was lower, and KYN and 3-IS concentrations were higher than in the control group. A negative correlation was found between the S-score and urinary concentration of 5-HIAA (p < 0.001), and 3-IS concentration was positively correlated with the S-score. However, the correlation between the S-score and 3-IS concentration was negative (p < 0.01). After a dietary intervention, 5-HIAA concentration increased in both groups, and the severity of symptoms decreased, but the decrease was more pronounced in Group IIB. (4) Conclusion: A low FODMAP diet supplemented with L-tryptophan has beneficial effects in elderly patients suffering from functional constipation.