Packaging materials are subject to risk assessment since they can transfer their components to the food, and they may constitute a risk for the consumers’ health. Therefore, estimating the exposure to chemicals migrating from packaging is required. In this study, a novel approach based on a total diet study (TDS)-like investigation to evaluate the exposure to chemicals transferred from the packaging was presented. The proposed methodology involved a non-targeted gas chromatography coupled to mass spectrometry (GC-MS) method to identify potential migrants and the determination of the migrants in composite food samples. The method was applied to evaluate the dietary exposure to chemicals from food packaging materials used for milk and dairy products in the Spanish child and adolescent populations. Several migrants identified in packaging materials were selected to determine their concentration in composite food samples. These chemicals included diethyl phthalate (DEP), diisobutyl phthalate (DIBP), dibutyl phthalate (DBP), bis(2ethylhexyl) phthalate (DEHP), benzophenone (BP), 1,3-diphenylpropane (1,3-DPP), and bis(2-ethylhexyl) terephthalate (DEHT). The method exhibited a good sensitivity (limit of detection, LOD ≤ 0.05 µg/g) and a satisfactory recovery (78.4-124%). Finally, the exposure was estimated using the Spanish national dietary survey ENALIA. Phthalates DBP and DEHP showed the highest mean exposure, ranging from 2.42 (10–17 years)–4.40 (12–35 months) and 1.35 (10–17 years)–4.07 (12–35 months) µg/kg bw/day for DBP and DEHP, respectively.