An observer that obtains estimates of the translational and rotational motion states for a rigid body under the influence of known forces and moments is presented. This nonlinear observer exhibits almost global convergence of state estimates in finite time, based on state measurements of the rigid body's pose and velocities. It assumes a known dynamics model with known resultant force and resultant torque acting on the body, which may include feedback control force and control torque. The observer design based on this model uses the exponential coordinates to describe rigid body pose estimation errors on SE(3), which provides an almost global description of the pose estimate error. Finite-time convergence of state estimates and the observer are shown using a Lyapunov analysis on the nonlinear state space of motion. Numerical simulation results confirm these analytically obtained convergence properties for the case that there is no measurement noise and no uncertainty (noise) in the dynamics. The robustness of this observer to measurement noise in body velocities and additive noise in the force and torque components is also shown through numerical simulation results.