In managed pressure drilling, there are two main challenges involved. First, the bottomhole pressure and flow rate to be controlled is updated at a low rate, which can be viewed as unmeasured. Second, the drilling process is subject to unknown parameters (e.g., frictions, densities), unmodeled dynamics and noise. To deal with these issues, this paper presents an integrated fast estimation and ℒ1 adaptive control scheme. The estimator provides fast estimation of the bottomhole pressure based on the available measurements. The ℒ1 adaptive controller drives the pressure to the desired value following a reference model. The design is based on a recently developed nonlinear drilling model. The results demonstrate that the ℒ1 adaptive controller has guaranteed performance bounds for both the input and the output signals of the system while using the estimation of the regulated outputs. Simulations that include different operational conditions verify the theoretical findings.