The maintenance of stable plasma drug concentrations within a therapeutic window can be critical for drug efficacy. Here, we developed a wearable osmotic microneedle (OMN) patch to support sustained drug dosing for at least 24 hours without the use of electronic components. The OMN patch uses an osmotic pressure driving force to deliver drug solution into the skin through three hollow microneedles with diameters of less than 200 micrometers. The rate of drug release was related to the composition and concentration of the osmogen and drug and to the physical properties of the semipermeable membrane separating the low- and high-solute compartments. The OMN patch released the peptide drug exenatide in rats and mice for 24 hours, whereas subcutaneous injection resulted in a burst release and rapid decline in the plasma drug concentration. OMN release of exenatide improved glycemic control in a diabetic mouse model consistent with a sustained effective plasma concentration of the drug. Continuous release of the small-molecule chemotherapeutic drug cytarabine reduced the progression of acute myeloid leukemia in mice more effectively than subcutaneous injection. Further evaluation of the OMN patch in canines demonstrated continuous dosing of cytarabine up to 225 milligrams for 24 hours, satisfying clinical requirements (150 to 300 milligrams daily). OMN patches were well tolerated in human participants with minimal pain or irritation of the skin and a stated preference over other administration routes. This wearable drug delivery system could provide a platform for stable high-dose drug release with convenience and safety.