Excess in growth hormone (GH) levels, seen in patients with acromegaly, is associated with increases in fractures. This happens despite wider bones and independent of bone mineral density. We used the bovine GH (bGH) transgenic mice, which show constitutive excess in GH and insulin‐like growth factor 1 (IGF‐1) in serum and tissues, to study how lifelong increases in GH and IGF‐1 affect skeletal integrity. Additionally, we crossed the acid labile subunit (ALS) null (ALSKO) to the bGH mice to reduce serum IGF‐1 levels. Our findings indicate sexually dimorphic effects of GH on cortical and trabecular bone. Male bGH mice showed enlarged cortical diameters, but with marrow cavity expansion and thin cortices as well as increased vascular porosity that were associated with reductions in diaphyseal strength and stiffness. In contrast, female bGH mice presented with significantly smaller‐diameter diaphysis, with greater cortical bone thickness and with a slightly reduced tissue elastic modulus (by microindentation), ultimately resulting in overall stronger, stiffer bones. We found increases in C‐terminal telopeptide of type 1 collagen and procollagen type 1 N propeptide in serum, independent of circulating IGF‐1 levels, indicating increased bone remodeling with excess GH. Sexual dimorphism in response to excess GH was also observed in the trabecular bone compartment, particularly at the femur distal metaphysis. Female bGH mice preserved their trabecular architecture during aging, whereas trabecular bone volume in male bGH mice significantly reduced and was associated with thinning of the trabeculae. We conclude that pathological excess in GH results in sexually dimorphic changes in bone architecture and gains in bone mass that affect whole‐bone mechanical properties, as well as sex‐specific differences in bone material properties. © 2022 American Society for Bone and Mineral Research (ASBMR).