Two categories of bone disease, osteoporosis and osteomalacia, affect bone in different ways: bone mineral and matrix are lost in roughly equal proportions in osteoporosis, while only mineral is depleted in osteomalacia. The difference between these disorders is in bone mineralization: the mass of mineral per volume of bone matrix, excluding pore spaces. Standard clinical examinations measure x-ray attenuation to infer mineral density. However, bone mineral density alone cannot fully describe bone health. Advances in solid-state 31P and 1H magnetic resonance imaging (MRI) have enabled quantification of the densities of extremely short-lived bone mineral 31P and matrix-bound water 1H signals as surrogates for bone mineral and matrix densities. The ratio of these two measurements provides the degree of mineralization of bone (DMB). In this dissertation, the relaxation properties of bone mineral 31P and water 1H were analyzed, the surrogacy of bound water concentration for bone matrix density was established, and measurements of bone mineral 31P and matrix-associated water 1H densities in human bone specimens were designed and implemented on clinical scanners. Although bone mineral 31P longitudinal relaxation time (T1) increased and effective transverse relaxation time (T2*) decreased with increasing field strength, the predicted signal-to-noise ratio (SNR) increased slightly. Also, the short-T2* fraction of bone water calculated by 1H bi-component fitting was correlated with porosity and matrix density at 1.5 T, but these associations weakened as field strength increased. In contrast, short-transverse relaxation time (T2) fraction was highly correlated with gold-standard measurements, suggesting the superiority of T2-based methods for separation of bound and pore water fractions. Additionally, single adiabatic inversion-recovery zero echo time (SIR-ZTE) 1H density was correlated negatively with porosity and positively with matrix and mineral densities, suggesting that this MRI method provides a surrogate measure of bone matrix density. Finally, both bone mineral 31P and matrix-associated 1H densities in human cortical bone specimens were correlated negatively with porosity and age, and positively with peripheral quantitative computed tomography (pQCT) density. As expected, DMB was uncorrelated with porosity, age, or pQCT density. This work established the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware.