Rye (Secale cereale L., 2n=2x=14, RR) is a significant genetic resource for improving common wheat because of its resistance to multiple diseases and abiotic-stress tolerant traits.  The 1RS chromosome from the German cultivated rye variety Petkus is critical in wheat breeding.  However, its weakened disease resistance highlights the need to identify new resources.  In the present study, a novel derived line called D27 was developed from common wheat and Mexico Rye.  Cytological observations characterized the karyotype of D27 as 2n=42=21 II.  Genomic in situ hybridization indicated that a pair of whole-arm translocated Mexico Rye chromosomes were inherited typically in the mitotic and meiosis stages of D27.  Experiments using fluorescence in situ hybridization (FISH) and gliadin electrophoresis showed that D27 lacked wheat 1DS chromosomes.  They were replaced by 1RS chromosomes of Mexico Rye, supported by wheat simple-sequence repeat markers, rye sequence characterized amplified region markers, and wheat 40K SNP array analysis.  The wheat 1DS chromosomes could not be detected by molecular markers and wheat SNP array, but the presence of rye 1RS chromosomes was confirmed.  Agronomic trait assessments indicated that D27 had a higher tiller number and enhanced stripe rust and powdery mildew resistance.  In addition, dough properties analysis showed that replacing 1DS led to higher viscosity and lower dough elasticity in D27, which was beneficial for cake making.  In conclusion, the novel cytogenetically stable common wheat–Mexico Rye T1DL·1RS translocation line D27 offers excellent potential as outstanding germplasm in wheat breeding programs focusing on disease resistance and yield improvement.  Additionally, it can be valuable for researching the rye 1RS chromosome’s genetic diversity.