Background: It is well-documented that (bio)chemical reaction capacity of raw potato starch depends on crystallinity, morphology and other chemical and physical properties of starch granules, and these properties are closely related to gene functions. Preparative yield, amylose/amylopectin content, and phosphorylation of potato tuber starch are starch-related traits studied at the genetic level. In this paper, we perform a genome-wide association study using a 22K SNP potato array to identify for the first time genomic regions associated with starch granule morphology and to increase number of known genome loci associated with potato starch yield. Methods: A set of 90 potato (Solanum tuberosum L.) varieties from the ICG “GenAgro” collection (Novosibirsk, Russia) was harvested, 90 samples of raw tuber starch were obtained, and DNA samples were isolated from the skin of the tubers. Morphology of potato tuber starch granules was evaluated by optical microscopy and subsequent computer image analysis. A set of 15,214 scorable SNPs was used for the genome-wide analysis. In total, 53 SNPs were found to be significantly associated with potato starch morphology traits (aspect ratio, roundness, circularity, and the first bicomponent) and starch yield-related traits. Results: A total of 53 novel SNPs was identified on potato chromosomes 1, 2, 4, 5, 6, 7, 9, 11 and 12; these SNPs are associated with tuber starch preparative yield and granule morphology. Eight SNPs are situated close to each other on the chromosome 1 and 19 SNPs—on the chromosome 2, forming two DNA regions—potential QTLs, regulating aspect ratio and roundness of the starch granules. Thirty-seven of 53 SNPs are located in protein-coding regions. There are indications that granule shape may depend on starch phosphorylation processes. The GWD gene, which is known to regulate starch phosphorylation—dephosphorylation, participates in the regulation of a number of morphological traits, rather than one specific trait. Some significant SNPs are associated with membrane and plastid proteins, as well as DNA transcription and binding regulators. Other SNPs are related to low-molecular-weight metabolite synthesis, and may be associated with flavonoid biosynthesis and circadian rhythm-related metabolic processes. The preparative yield of tuber starch is a polygenic trait that is associated with a number of SNPs from various regions and chromosomes in the potato genome.