The application of embryonic stem cells (ESCs) in bone tissue engineering and regenerative medicine requires the development of suitable bioprocesses that facilitate the integrated, reproducible, automatable production of clinically-relevant, scaleable, and integrated bioprocesses that generate sufficient cell numbers resulting in the formation of three-dimensional (3D) mineralised, bone tissue-like constructs. Previously, we have reported the enhanced differentiation of undifferentiated mESCs toward the osteogenic lineage in the absence of embryoid body formation. Herein, we present an efficient and integrated 3D bioprocess based on the encapsulation of undifferentiated mESCs within alginate hydrogels and culture in a rotary cell culture microgravity bioreactor. Specifically, for the first 3 days, encapsulated mESCs were cultured in 50% (v/v) HepG2 conditioned medium to generate a cell population with enhanced mesodermal differentiation capability followed by osteogenic differentiation using osteogenic media containing ascorbic acid, beta-glycerophosphate and dexamethasone. 3D mineralised constructs were generated that displayed the morphological, phenotypical, and molecular attributes of the osteogenic lineage, as well mechanical strength and mineralised calcium/phosphate deposition. Consequently, this bioprocess provides an efficient, automatable, scalable and functional culture system for application to bone tissue engineering in the context of macroscopic bone formation.