Summary In this paper, an L1 adaptive output‐feedback descriptor is designed for multivariable nonlinear systems with measurement noises. If the system is detectable, noises are bounded, and some rank conditions are satisfied, an L1 adaptive output‐feedback descriptor is constructed to asymptotically estimate states, nonlinear uncertainties, and measurement noises at the same time deliver a good tracking performance. The original system is augmented with all the system states and measurement noises; two design parameters provide additional degrees of freedom. The freedom of selecting these parameters allows us to choose the derivative gain to reduce the noise amplification and the proportional gain to ensure the stability of the estimated error dynamics. An adaptive law will update the adaptive parameters that represent the uncertainty estimates such that the estimation error between the predicted state and the real state is driven to zero at every integration time step. Of course, neglection of the unknowns for solving the error dynamic equations will introduce an estimation error in the adaptive parameters. The magnitude of this error can be lessened by choosing a proper sampling time. The two design parameters and adaptive law guarantee the performance bounds for the estimation errors, both states and control signals. A control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. Numerical examples are given to illustrate the design procedures, and the simulation results demonstrate the availability and feasibility of the developed framework.