In this paper, we are concerned with an initial boundary value problem of wave equations incorporating strong damping and structural damping. By virtue of semigroup theory, we establish the global well-posedness of weak solutions, where the nonlinear damping and source terms satisfy subcritical growth conditions. Furthermore, based on Nakao's inequality, we derive the exponential decay estimate of solutions. Notably, we relax the constraints on the coefficients of structural damping to a general non-negativity condition.