Intensely pigmented potato tubers are desired for the speciality potato market because of the health-promoting effects of pigments and other related compounds. Although highly coloured potatoes show higher concentrations of carotenoids and anthocyanins and higher antioxidant capacity, the phytochemical composition is highly dependent on environmental factors. Thus, the effects of genotype, environment and genotype × environment interactions on monomeric anthocyanins, soluble phenolics, carotenoids and hydrophilic antioxidant capacity were evaluated in a set of cultivars selected on the basis of the contrasting flesh colour of tubers. Twenty-one tetraploid potato genotypes were grown in three different field trials at Arkaute and Iturrieta for 2 years. Genotype, environment and genotype × environment interactions were significant for all of the studied parameters (P ≤ 0.01). However, most of the variation was accounted for by clonal variation. Broad-sense heritabilities (and their 95% confidence intervals) were 0.947 (0.832–0.981) for total monomeric anthocyanins, 0.917 (0.852–0.952) for total soluble phenolics, 0.950 (0.911–0.975) for total carotenoids, and 0.887 (0.799–0.945) and 0.850 (0.734–0.927) for hydrophilic antioxidant capacity measured by ABTS and DPPH methods, respectively. Although certain instabilities were recorded for all of the studied traits, the high estimates of heritability support the main role of genetics in phytochemical composition and suggest that sufficient heritable genetic variation exists in tetraploid potato germplasm for the breeding of advanced clones with improved bioactive properties.