Plant roots play a fundamental role in maintaining soil health. Although a broad range of root traits have been reported, few studies have attempted to link root morphology with soil structure. Here, we used shovelomics to characterize the root morphology of a wheat cultivar (Paragon), and two landraces (Senatore-Cappelli, and Watkins238), and advanced soil pore and root network X-ray computed tomography to assess their impact on soil morphology at cylinder and aggregate scales. Bare soil was analyzed as a control. Minkowski functionals and percolation theory parameters were computed to characterize soil pore network morphology. Bioporosity at the cylinder scale was significantly different for all cultivars compared to the bare soil. Bare soil presented the largest structural pore volume and the smallest biopore volume, this suggesting rapid degradation of biopores. At the cylinder scale, biopore characteristics were significantly different between Senatore-Cappelli and Watkins238, with Senatore-Cappelli exhibiting more pores with diameters >1 mm. The parameters from percolation theory revealed notable differences between the rhizospheric and bare soil samples. We found significant differences between genotypes, finding statistically significant correlations among root morphology parameters and pore network geometry. Total imaged porosity and total root volume were limited descriptors of the effect of roots on soil structure, which is better quantified by pore network connectivity measurements. Our findings confirm previous studies on the relationship between root traits and soil properties and highlight the potential of our experimental approach to explore how different genotypes may influence soil morphology, paving the way for future applications in plant phenotyping.