Genomic selection (GS) is becoming increasingly applicable to crops as the genotyping costs continue to decrease, which makes it an attractive alternative to traditional selective breeding based on observed phenotypes. With genome-wide molecular markers, selection based on predictions from genotypes can be made in the absence of direct phenotyping. The reliability of predictions depends strongly on the number of individuals used for training the predictive algorithms, particularly in a highly genetically diverse organism such as potatoes; however, the relationship between the individuals also has an enormous impact on prediction accuracy. Here we have studied genomic prediction in three different panels of potato cultivars, varying in size, design, and phenotypic profile. We have developed genomic prediction models for two important agronomic traits of potato, dry matter content and chipping quality. We used genotyping-by-sequencing to genotype 1,146 individuals and generated genomic prediction models from 167,637 markers to calculate genomic estimated breeding values with genomic best linear unbiased prediction. Cross-validated prediction correlations of 0.75-0.83 and 0.39-0.79 were obtained for dry matter content and chipping quality, respectively, when combining the three populations. These prediction accuracies were similar to those obtained when predicting performance within each panel. In contrast, but not unexpectedly, predictions across populations were generally lower, 0.37-0.71 and 0.28-0.48 for dry matter content and chipping quality, respectively. These predictions are not limited by the number of markers included, since similar prediction accuracies could be obtained when using merely 7,800 markers (<5%). Our results suggest that predictions across breeding populations in tetraploid potato are presently unreliable, but that individual prediction models within populations can be combined in an additive fashion to obtain high quality prediction models relevant for several breeding populations.