Quinoa (Chenopodium quinoa) and kiwicha (Amaranthus caudatus) are nutritious pseudocereals that originate from the Andean region. The aim of this research was to study the effect of germination and the subsequent kilning on the phenolic compounds and proximate composition in selected Peruvian varieties of quinoa (“Chullpi”) and kiwicha (“Oscar Blanco”). The germination process was carried out for 24, 48 and 72 h at 22 °C, and the kilning was performed with samples germinated for 72 h by drying the seeds at 90 °C for 5 min. Both processes increased the protein content of the samples. However, lipid content was reduced during germination. On the other hand, germination and kilning clearly increased the concentration of total phenolic compounds in both quinoa and kiwicha. Germination for 72 h either with or without kilning process resulted in a significant (p < 0.05) increase in the total content of phenolics compared to untreated materials, which was especially due to coumaric acid and a kaempferol tri-glycoside in quinoa and caffeoylquinic acid in kiwicha. Based on the results, germination and kilning may improve the nutritional quality of the Andean grains, encouraging the usage of the processed grains as ingredients in functional products for people with special gluten-free or vegetarian diets.