The efficacy of implanted biomedical devices is often compromised by host recognition and subsequent foreign body responses. Here, we demonstrate the role of the geometry of implanted materials on their biocompatibility in vivo. In rodent and non-human primate animal models, implanted spheres 1.5 mm and above in diameter across a broad spectrum of materials, including hydrogels, ceramics, metals and plastics, significantly abrogated foreign body reactions and fibrosis when compared with smaller spheres. We also show that for encapsulated rat pancreatic islet cells transplanted into streptozotocin-treated diabetic C57BL/6 mice, islets prepared in 1.5-mm alginate capsules were able to restore blood-glucose control for up to 180 days, a period more than five times longer than for transplanted grafts encapsulated within conventionally sized 0.5-mm alginate capsules. Our findings suggest that the in vivo biocompatibility of biomedical devices can be significantly improved simply by tuning their spherical dimensions.