Mango fruit is a rich source of bioactive compounds such as carotenoids, phenolics, and ascorbic acid. This research aimed at predicting the content of these bioactive compounds in ‘Tommy Atkins’ mangoes using optical properties, i.e., the absorption coefficients related to chlorophylls (µa630, µa650, µa670, µa690) and carotenoids (µa540), and the scattering parameters (Mie’s A and b), measured during the shelf-life period at 20 °C by time-resolved reflectance spectroscopy. The µa540 and Mie’s b increased during shelf-life, while µa670 and Mie’s A decreased. Ascorbic acid (AA) and the total antioxidant capacity decreased during shelf-life, while the total carotenoids increased, and the total phenols (TPC) did not significantly change. The major constituent of the nonsaponified extracts, (all-E)-β-carotene, increased during the shelf-life period. A similar trend was observed for the total (all-E)-violaxanthin esters, the total (9Z)-violaxanthin esters and the total neoxanthin esters. Carotenoids are responsible for the yellow-orange color of mangoes: (all-E)-β-carotene was mainly related to a* and h° pulp color while the total (all-E)-violaxanthin esters were mainly linked to b*, C*, and the yellowness index. Using multiple regression analysis, good prediction models were achieved for the total carotenoids (R2adj = 83.1%), the total xanthophylls (R2adj = 78%), (all-E)-β-carotene (R2adj = 77%) and the total (all-E)-violaxanthin esters (R2adj = 74%), while less satisfactory predictions were obtained for AA and TPC.