Stem cells isolated from the Wharton’s jelly of the human umbilical cord (hWJSCs) are unique compared to other stem cell types as they lie in between embryonic stem cells (ESCs) and adult mesenchymal stem cells (MSCs) on the developmental map and share stemness markers of ESCs and MSCs. Yet, they do not induce tumorigenesis and are hypoimmunogenic and proliferative and fresh cell numbers can be harvested painlessly in abundance from discarded umbilical cords. Additionally, they secrete important soluble bioactive molecules from the interleukin and cell adhesion family, hyaluronic acid, collagen, glycosoaminoglycans, and chondroitin sulfate. Many of these molecules are involved in bone, cartilage, and joint repair. It has also been shown that hWJSCs attach, proliferate, and differentiate efficiently in the stem cell niches of three-dimensional matrices, particularly nanofibrous scaffolds. Thus, tissue constructs made up of hWJSCs and biodegradable nanofibrous scaffolds will facilitate clinical translation and improved functional outcome for arthritis, bone, and cartilage diseases. When applied in vivo, the hWJSCs from the tissue construct may improve repair either by differentiating into new chondrocytes or osteocytes and/or release of important factors that favor repair through paracrine functions. The nanofibrous scaffold is expected to provide the architecture and niches for the hWJSCs to perform and will later biodegrade encouraging engraftment. This chapter provides a step-by-step protocol for the preparation of such tissue constructs involving hWJSCs and nanofibrous scaffolds. The methodology also includes the targeted in vitro differentiation of the hWJSCs to osteogenic and chondrogenic lineages when attached to the nanofibrous scaffolds.