Tuber dormancy and sprouting are commercially important potato traits as long-term tuber storage is necessary to ensure year-round availability. Premature dormancy release and sprout growth in tubers during storage can result in a significant deterioration in product quality. In addition, the main chemical sprout suppressant chlorpropham has been withdrawn in Europe, necessitating alternative approaches for controlling sprouting. Breeding potato cultivars with longer dormancy and slower sprout growth is a desirable goal, although this must be tempered by the needs of the seed potato industry, where dormancy break and sprout vigour are required for rapid emergence. We have performed a detailed genetic analysis of tuber sprout growth using a diploid potato population derived from two highly heterozygous parents. A dual approach employing conventional QTL analysis allied to a combined bulk-segregant analysis (BSA) using a novel potato whole-exome capture (WEC) platform was evaluated. Tubers were assessed for sprout growth in storage at six time-points over two consecutive growing seasons. Genetic analysis revealed the presence of main QTL on five chromosomes, several of which were consistent across two growing seasons. In addition, phenotypic bulks displaying extreme sprout growth phenotypes were subjected to WEC sequencing for performing BSA. The combined BSA and WEC approach corroborated QTL locations and served to narrow the associated genomic regions, while also identifying new QTL for further investigation. Overall, our findings reveal a very complex genetic architecture for tuber sprouting and sprout growth, which has implications both for potato and other root, bulb and tuber crops where long-term storage is essential.