Wheat is of significant economic importance due to its high yield potential and high nutritional value as well as the technological usefulness of the grain. Field experiments were carried out in the years 2015–2018 in southeastern Poland. A three-factor experiment was used to study the influence of wheat cultivars (hybrid—cvs. Hybred and Hymack; common—cv. Batuta), cultivation systems (organic—ORG, integrated—INT, conventional—CON) and of environmental conditions (using two different locations: Dukla and Nowy Lubliniec) on wheat grains’ phenolic acid (PA) content and grain yield. The research confirms the genetic determinants of grain yield and PA composition in wheat grains, and their different accumulation levels of ferulic acid and other PAs—with the exception of sinapic, p-coumaric, and salicilic—with hybrid cultivars performing better than common cultivars. The ORG system, compared to the INT and CON systems, caused a larger increase in total acids (TPAs)—especially of ferulic, vanillic, and syringic acids—in grains of cv. Hybred, and of caffeic acid in cv. Hymack, compared to cv. Batuta. The lack of interaction between the cultivation systems and the cultivars indicates that similar reactions to increases in grain yield due to increases in the intensity of cultivation take place in cultivars. The more favourable environmental conditions in Dukla favoured the accumulation of ferulic, p-coumaric, vanillic, syringic, p-hydroxybenzoic, and protocatechuic acids in the grains. TPAs were higher by 4.3% and the grain yield by 4.0% on average. Variable conditions in the season 2015/2016 resulted in higher yields of hybrid cvs. grains than of common cv., which proves the greater yielding stability of these cultivars in years with adverse weather conditions. The season 2016/2017 had less rainfall and faced high temperatures during grain ripening, favouring a higher PA content and TPAs, especially in the grains of cv. Hybred. This suggests a need to further assess the genetic progress of hybrid wheat cultivars cultivated under different environmental conditions in terms of their PA composition and content.