The Moving Morphable Component (MMC) method, characterized by its explicit geometric description, enables seamless integration between optimization results and Computer-Aided Design (CAD) models, thereby demonstrating significant potential for engineering applications. However, the ersatz material model within the conventional MMC framework typically relies on a Heaviside function-based numerical projection strategy to formulate element densities. This approach introduces hyperparameters that lack clear physical interpretation and are highly empirical. Consequently, it often leads to biased element density estimations, resulting in discrepancies between the design and physical models, as well as issues such as spurious connectivity. To address these challenges, this paper proposes a hyperparameter-free topology optimization approach termed Analytical Density Integration MMC (ADI-MMC). By exploiting the local linearity of the Topological Description Function (TDF), this method derives a closed-form analytical solution for the component volume/area fraction within finite elements. This fundamentally eliminates design biases and numerical instabilities associated with artificial parameters. Numerical examples demonstrate that the proposed ADI-MMC method exhibits superior numerical stability and robustness. It significantly outperforms conventional methods in minimizing objective function values and enhancing convergence stability, thereby achieving high consistency between the geometric and finite element models.