Disturbance covariance estimation is a centrally important problem in radar space time adaptive processing (STAP). Because training is invariably scarce, estimators that exploit inherent structure and physical radar constraints are needed in practice. This paper develops a new computationally efficient estimator which obtains a Toeplitz approximation of the structured interference covariance under a rank constraint. Previous work has shown that exact ML estimation of Toeplitz covariance matrix has no closed form solution and most versions of this problem result in iterative estimators which are computationally expensive. Our proposed solution focuses on a computationally efficient approximation and involves a cascade of two closed form solutions. First, we obtain the rank constrained ML estimator (RCML) whose merits have recently been established firmly for radar STAP. The central contribution of this paper is the rank preserving Toeplitz approximation, which we demonstrate can be modeled as an equality constrained quadratic program and also admits a closed form. Extensive performance evaluation on both simulated and KASSPER data confirms that the proposed estimator yields unbeatable performance for radar STAP under the previously stated conditions of rank and Toeplitz constraints.