Stable and effective enforcement of hard constraints is one of the crucial components in controlling physics-based dynamic simulation systems. The conventional explicit Baumgarte constraint stabilization confines the time step to be within a stability limit and requires users to pick problem-dependent coefficients to achieve fast convergence or to prevent oscillations. The recently proposed post-stabilization method has shown a successful constraint drift reduction but it does not guarantee the physically correct behavior of motion and requires additional computational cost to decrease the constraint errors. This paper presents our new implicit constraint enforcement technique that is stable over large time steps and does not require problem dependent stabilization parameters. This new implicit constraint enforcement method uses the future time step to estimate the correct magnitude of the constraint forces, resulting in better stability over bigger time steps. More importantly, the proposed method generates physically conforming constraint forces while minimizing the constraint drifts, resulting in physically correct motion. Its asymptotic computational complexity is same as the explicit Baumgarte method. It can be easily integrated into various constrained dynamic systems including rigid body or deformable structure applications. This paper describes a formulation of implicit constraint enforcement and an accumulated constraint error and dynamic behavior analysis for comparison with existing methods.