Reclaimed water (RW) is widely used in agricultural systems; however, it affects soil properties and the surrounding environment, thus influencing soil nitrogen transformation and increasing N2O and NO emissions. Understanding the influencing mechanism of N2O production in RW-irrigated soil is very important for water resource utilization and environmental protection, but it is rarely studied. This study investigated the impact of three nitrogen ions (NH4+, NO3−, NO2−) on the nitrogen transformation process and non-biological processes affecting NO and N2O emissions from soil under multiyear RW-irrigated conditions. The results showed that RW effectively increased the abundance of nitrifying and denitrifying functional genes, leading to a significant increase (p < 0.05) in soil NO and N2O emissions under ammonium treatment. Furthermore, RW can reduce the cumulative NH3 emission by 19.11% compared to deionized water (DW). In nitrate treatment, RW can significantly increase (p < 0.05) the nitrate conversion rate by increasing the abundance of denitrifying genes, but not significantly enhance N2O and NO emissions. In NO2− oxidation, RW could increase the abundance of nitrifying genes (AOA-amoA, AOB-amoA), thereby promoting the progression of nitrifier denitrification and leading to a substantial increase (p < 0.05) in soil N2O production. In summary, RW irrigation primarily increases N2O emissions from soil by enhancing soil autotrophic nitrification and heterotrophic nitration. To effectively control soil N2O emissions under agricultural irrigation with RW, it is crucial to carefully manage soil nitrification and adjust the ratio of ammonium and nitrate in the soil.