Strategic management of crop residues is essential to enhance soil quality for sustainable agriculture. However, little is known about the specific amounts of crop residues needed to improve soil quality characteristics which are key to develop economic plans. In this study, we investigated the effects of applying crop residue at five rates, including 100% (R100), 75% (R75), 50% (R50), 25% (R25), and 0% (R0), on wheat yield and soil properties. Field experiments were conducted for two cropping seasons in a wheat-corn rotation under conventional (CT) and no-till (NT) systems to observe the first results obtained during short-term periods (one-year application). During the study, the wheat and corn fields were irrigated. Application of plant residue resulted in increased soil organic carbon (SOC) and available nutrients and improved soil physical properties, i.e., aggregates mean weight diameter in wet (MWDw) and dry (MWDd) conditions, water-stable aggregates (WSA), dry-stable aggregates, (DSA), soil water infiltration (SWI), soil available water (SAW), and yield of wheat and corn. The effects were stronger at higher residue application rates. In the CT system, compared to R0, R100 resulted in the highest increase equal to 38, 29, 23, 34, 35, 41, and 11% for SOC, MWDw, MWDd, WSA, DSA, SAW, and wheat grain yield, respectively. This was equivalent to 28, 19.5, 19, 37, 44, 52, and 6% for the NT system, respectively. Generally, the NT system resulted in a stratification of the soil properties within 0–10 cm compared to 10–20 cm soil depth, but a uniform distribution for both depths under CT system. Overall, these results show that crop residue application can improve soil quality and yield in cereal production systems under semi-arid conditions during the first year of application. It will be key to monitor these changes in along-term field studies.