In this work, physical cross-linking was used to create nanocomposite hydrogels composed of unmodified gum arabic (GA), chitosan (Ch), and natural nanohydroxyapatite (nHA), using an acrylic acid (AA) solvent. Different GA/chitosan contents (15%, 25%, and 35% of the used AA) as well as different nHA contents (2, 5, and 10 wt.%), were used and studied. The natural nHA and the fabricated GA/Ch/nHA nanocomposite hydrogels were characterized using different analysis techniques. Using acrylic acid solvent produced novel hydrogels with compressive strength of 15.43–22.20 MPa which is similar to that of natural cortical bone. The addition of natural nHA to the hydrogels resulted in a significant improvement in the compressive strength of the fabricated hydrogels. In vitro studies of water absorption and degradation—and in vivo studies—confirmed that the nanocomposite hydrogels described here are biodegradable, biocompatible, and facilitate apatite formation while immersed in the simulated body fluid (SBF). In light of these findings, the GA/Ch/nHA nanocomposite hydrogels are recommended for preparing bioactive nanoscaffolds for testing in bone regeneration applications.