The culinary poppy (Papaver somniferum L.) has been used for centuries in everyday diets, especially for food, but also as a non-food source of health-promoting ingredients. In the present study, a field trial was set with white-seeded poppy varieties collected from farmers in Croatia. The poppies were sown as a winter crop. Selenium biofortification was applied using different selenium sources, such as selenite, SeO32−, and selenate SeO42−. In the flowering stage, biofortification was carried out as follows: (1) Se-0: control; (2) SeO3_30: 30 g ha−1; (3) SeO3_60: 60 g ha−1; (4) SeO4_30: 30 g ha−1; and (5) SeO4_60: 60 g ha−1. Plants formed an average of four capsules per plant, with an average seed mass per capsule of 3.52 g. The seed yield varied from 0.91 (SeO3_30) to 1.26 t ha−1 (SeO4_30). The cold-pressed oil was characterized as good-quality since the average water content was 0.38%, insoluble impurities consisted of 0.013%, iodine number value was 135.81 g, I2 was 100 g−1, and saponification number was 188.51 mg KOH g−1, and it was on average 0.93% free fatty acids. Selenium biofortification had a significant (p ≤ 0.05) impact on Se accumulation in the seeds. Thus, the selenite form increased Se content in the seeds by about 7% compared to the control, whereas for the (4) SeO4_30 treatment, the increase was about 50%, and for (5) SeO4_60, it was even higher, about 91% compared to the control treatment. The highest content of fatty acids in the cold-pressed oil was determined for linoleic (76.31%), oleic (13.49), and palmitic (7.86%) acids.