Low organic matter content is one of the main constraints in arid and semiarid regions. This constraint and its negative influences on soils and plant growth may be alleviated by biochar (BC). Furthermore, improving soil physical and hydraulic attributes by application of biochar has received increased attention. Therefore, in the present study, the effects of sugarcane bagasse-derived biochar on the structural stability, water availability, and pore-size distribution (PSD) of three texturally different calcareous soils collected from different agro-climatologically regions were examined during a long-term experiment. Low and high-temperature biochars, produced in a muffle furnace by the traditional slow pyrolysis method at 300 °C (BC300) and 600 °C (BC600) were evaluated. Pots (15 kg) were filled with three different silty-clay Inceptisols (SCInc), silty-clay-loam Alfisols (SCLAlf), and loam Aridisols (LArid) soils mixed with 0 (control), 1, 2, and 3 w/w% of BC300 and BC600 during 540 days of incubation. The high energy moisture characteristic (HEMC) data was modeled using a modified van Genuchten function to quantify aggregate stability through stability ratio (SR) and structural stability index (SSI). The plant available water (PAW), least limiting water range (LLWR), and integral water capacity (IWC) were calculated with two matric suctions (h) of 330 cm for field capacity (FC) and 15,000 cm for permanent wilting point (PWP). Then the integral energy (EI) values were calculated (EIIWC). Results indicated that the incorporation of 3 w/w% biochar significantly (p < 0.01) increased SR (35 to 100%) and SSI (21 to 28%) indices in all three soils. Biochar significantly increased modal suction (MS) in LArid soils (5 to 158%); whereas, decreased MS of the other soils (3 to 43%). MS, SR, and SSI of BC300 and BC600-treated soils were not significantly different. PAW, LLWR, and IWC significantly decreased in the SCInc (18 to 61%, 8 to 44%, and 6 to 35%) and SCLAlf (8 to 44%, 18 to 35%, and 20 to 47%) soils and increased in LArid (4 to 54%, 3 to 61%, and 24 to 111%) soil with increasing biochar doses. There were no changes in EIIWC in biochar-treated LArid soil where PAW, LLWR, and IWC increased. Biochar increased EIIWC across the studied soil from 1% to 3.38 folds, thereby increasing the gradient of water potential to absorb the available water. Soil and soil-biochar mixtures exhibited heterogeneous and multimodal pore-size distribution (PSD). Biochar promoted the PSD peaks related to water-transmitting pores in SCInc and SCLAlf soils while decreased in LArid soil. In conclusion, results indicated that among the applied levels of biochar, the application of 3 w/w% biochar is suggested as a suitable way to improve soil physical behavior and structural stability.