Time delay in attitude determination systems is unavoidable and it is usually caused by low-quality data sampling, poor sensor synchronization, momentary sensor outage or operational restrictions of sensors. Despite its performance-degrading effect, time delay has been widely neglected in the existing attitude estimation methods. This paper presents a general framework for design of attitude estimators with and without SO(3) manifold restriction by assuming that measurement of a single vector measurement is available with time delay. Also, measurement of rigid-body angular velocity is considered available with an unknown bias. The proposed estimator guarantees global and asymptotic convergence of attitude estimate to its true value. The observer gain is calculated by solving a delay-dependent matrix differential equation. Solvability of the differential equation depends on an observability condition related to the reference vectors. To illustrate performance of the proposed observer, we present simulation of a satellite system where the single delayed vector measurement is provided by a magnetometer. (C) 2016 Elsevier Ltd. All rights reserved.