The adaptive control design for linear stable plants with input magnitude and rate constraints is addressed. The proposed algorithm adopts the self-tuning regulator (STR) adaptive control principle with one-step-ahead control as its underlying control design. An important governing equation relating the prediction error to the 'input discrepancy' between adaptive control and the corresponding non-adaptive control is identified, independent of how the parameter estimates are attained. Together with the convergence property of least-square type estimation algorithm, the governing equation leads to a successful analysis on the convergence and tracking performance of the adaptive constrained one-step-ahead controller. Specifically, globally input matching property is maintained in the sense that the adaptive constrained control asymptotically matches its corresponding non-adaptive one. Furthermore, the desired tracking performance of the adaptive controller can be achieved asymptotically if the corresponding non-adaptive control is eventually out of the constraints. The proposed adaptive control is applicable to both minimum and non-minimum phase stable systems.