This experiment analyzed the effect of genetic determinants, the production technology, and the location on the nitrate and nitrites content in potato tubers directly after harvest. Nitrates and nitrites are anti-nutritional compounds, which limit or prevent the use of nutrients from consumed products and have a detrimental effect on the human body. The study was conducted on seven tetraploid potato (Solanum tuberosum L.) clones (’13-VIII-10’, ’13-VIII-27’, ’13-VIII-45 ‘, ’13-VIII-49’, ’13-VIII-50’, ’13-VIII-60’, ‘TG-97–403’), and three cultivars (‘Jelly’, ‘Satina’, and ‘Tajfun’) at four locations in Poland under either an integrated (Młochów, Boguchwała) or organic (Radzików, Chwałowice) production system. The results showed that the production system, location, and year significantly affected the nitrate and nitrites content in potatoes. Potato tubers originating from organic farming exhibited a lower content of the tested compounds (NO3ˉ—124.1 mg kg−1 FW; NO2ˉ—2.4 mg kg−1 FW) than that in the tubers obtained from an integrated production system (NO3ˉ—203.7 mg kg−1 FW, NO2ˉ—4.0 mg kg−1 FW). Under conditions of moderate stress as usual in the case of organic farming, the production of nitrates and nitrites are significantly lower than in the integrated production system. In our research potatoes from an integrated production system were characterised by a nitrate content at the limit of the established standard, i.e., 200 mg kg−1 FW. Tubers from the locality Chwałowice were characterised by the lowest nitrates and nitrites content, due to adequate environmental conditions, in addition to the best agricultural practice. The nitrates content depended to a greater extent on the environmental conditions than the potato on the genetic conditions. A higher content of nitrates and nitrites was found in the following potato clone 13-VIII-10 in Boguchwała from an integrated production system (NO3−—269.2 mg kg−1 F; NO2−—6.0 mg kg−1 FW), and in the ‘Tajfun’ cultivar (235.8; 5.8 mg kg−1 FW, respectively). Such a relationship was not found in integrated production in Młochów, which indicates the influence of the environment.